[{"month":"05","license":"https://creativecommons.org/licenses/by/4.0/","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","OA_place":"publisher","language":[{"iso":"eng"}],"quality_controlled":"1","article_processing_charge":"Yes","publication":"42nd International Symposium on Computational Geometry","citation":{"mla":"Adams, Henry, et al. “Lower Bounding the Gromov–Hausdorff Distance in Metric Graphs.” <i>42nd International Symposium on Computational Geometry</i>, vol. 367, 3:1-3:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.3\">10.4230/LIPIcs.SoCG.2026.3</a>.","ama":"Adams H, Majhi S, Manin F, Virk Z, Zava N. Lower bounding the Gromov–Hausdorff distance in metric graphs. In: <i>42nd International Symposium on Computational Geometry</i>. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.3\">10.4230/LIPIcs.SoCG.2026.3</a>","ieee":"H. Adams, S. Majhi, F. Manin, Z. Virk, and N. Zava, “Lower bounding the Gromov–Hausdorff distance in metric graphs,” in <i>42nd International Symposium on Computational Geometry</i>, New Brunswick, NJ, United States, 2026, vol. 367.","chicago":"Adams, Henry, Sushovan Majhi, Fedor Manin, Ziga Virk, and Nicolò Zava. “Lower Bounding the Gromov–Hausdorff Distance in Metric Graphs.” In <i>42nd International Symposium on Computational Geometry</i>, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.3\">https://doi.org/10.4230/LIPIcs.SoCG.2026.3</a>.","short":"H. Adams, S. Majhi, F. Manin, Z. Virk, N. Zava, in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","apa":"Adams, H., Majhi, S., Manin, F., Virk, Z., &#38; Zava, N. (2026). Lower bounding the Gromov–Hausdorff distance in metric graphs. In <i>42nd International Symposium on Computational Geometry</i> (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.3\">https://doi.org/10.4230/LIPIcs.SoCG.2026.3</a>","ista":"Adams H, Majhi S, Manin F, Virk Z, Zava N. 2026. Lower bounding the Gromov–Hausdorff distance in metric graphs. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 367, 3:1-3:16."},"date_published":"2026-05-27T00:00:00Z","conference":{"end_date":"2026-06-05","name":"SoCG: Symposium on Computational Geometry","location":"New Brunswick, NJ, United States","start_date":"2026-06-02"},"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"article_number":"3:1-3:16","intvolume":"       367","type":"conference","day":"27","acknowledgement":"Funding Henry Adams: Simons Foundation Travel Support for Mathematicians.\r\nŽiga Virk: Slovene research agency grant P1-0292.\r\nNicolò Zava: FWF Grant, Project number I4245-N35.\r\n","date_created":"2026-06-14T22:01:44Z","arxiv":1,"doi":"10.4230/LIPIcs.SoCG.2026.3","has_accepted_license":"1","status":"public","das_tickbox":"0","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959774185"]},"scopus_import":"1","ddc":["500"],"corr_author":"1","title":"Lower bounding the Gromov–Hausdorff distance in metric graphs","OA_type":"gold","department":[{"_id":"HeEd"}],"abstract":[{"text":"Let G be a finite, connected metric graph and let X be a subset of G. If X is sufficiently dense in G, we show that the Gromov-Hausdorff distance matches the Hausdorff distance, namely d_GH(G,X) = d_H(G,X). When the metric graph is the circle G = S¹ with circumference 2π, a recent study established the equality d_GH(S¹,X) = d_H(S¹,X) whenever d_GH(S¹,X) < π/6. Our results relax this hypothesis to d_GH(S¹,X) < π/3, and furthermore, we show that the constant π/3 is the best possible. We lower bound the Gromov-Hausdorff distance d_GH(G,X) by the Hausdorff distance d_H(G,X) via a simple topological obstruction: the existence of a possibly discontinuous function f: G → X with too small distortion contradicts the connectedness of G.","lang":"eng"}],"external_id":{"arxiv":["2411.09182"]},"author":[{"full_name":"Adams, Henry","first_name":"Henry","last_name":"Adams"},{"full_name":"Majhi, Sushovan","last_name":"Majhi","first_name":"Sushovan"},{"last_name":"Manin","first_name":"Fedor","full_name":"Manin, Fedor"},{"full_name":"Virk, Ziga","id":"2E36B656-F248-11E8-B48F-1D18A9856A87","first_name":"Ziga","last_name":"Virk"},{"first_name":"Nicolò","last_name":"Zava","full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"}],"oa":1,"oa_version":"Published Version","project":[{"name":"Algebraic Footprints of Geometric Features in Homology","grant_number":"I04245","_id":"26AD5D90-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"_id":"22003","publication_status":"published","year":"2026","volume":367,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"date_updated":"2026-06-22T08:43:47Z","file_size":1091310,"relation":"main_file","content_type":"application/pdf","file_id":"22115","file_name":"2026_LIPIcSSoCG_Adams.pdf","success":1,"creator":"dernst","checksum":"25d27c016409563196b8aecfe5bfdf41","date_created":"2026-06-22T08:43:47Z","access_level":"open_access"}],"file_date_updated":"2026-06-22T08:43:47Z","alternative_title":["LIPIcs"],"keyword":["Gromov–Hausdorff distance","distortion","connectedness","Borsuk–Ulam theorem"],"date_updated":"2026-06-22T08:49:17Z"},{"article_type":"original","page":"5153-5174","oa":1,"project":[{"name":"Algebraic Footprints of Geometric Features in Homology","grant_number":"I04245","_id":"26AD5D90-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"_id":"20867","oa_version":"Published Version","PlanS_conform":"1","department":[{"_id":"HeEd"}],"external_id":{"arxiv":["2303.04730"]},"author":[{"full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","first_name":"Nicolò","last_name":"Zava"}],"abstract":[{"lang":"eng","text":"We discuss the embeddability of subspaces of the Gromov–Hausdorff space, which consists of isometry classes of compact metric spaces endowed with the Gromov–Hausdorff distance, into Hilbert spaces. These embeddings are particularly valuable for applications to topological data analysis. We prove that its subspace consisting of metric spaces with at most n points has asymptotic dimension n(n−1)∕2. Thus, there exists a coarse embedding of that space into a Hilbert space. On the contrary, if the number of points is not bounded, then the subspace cannot be coarsely embedded into any uniformly convex Banach space and so, in particular, into any Hilbert space. Furthermore, we prove that, even if we restrict to finite metric spaces whose diameter is bounded by some constant, the subspace still cannot be bi-Lipschitz embedded into any finite-dimensional Hilbert space. We obtain both nonembeddability results by finding obstructions to coarse and bi-Lipschitz embeddings in families of isometry classes of finite subsets of the real line endowed with the Euclidean–Hausdorff distance."}],"file_date_updated":"2026-01-05T12:16:38Z","date_updated":"2026-01-05T12:19:09Z","volume":25,"year":"2025","publication_status":"published","file":[{"file_name":"2025_AlgebraicGeomTopology_Zava.pdf","content_type":"application/pdf","file_id":"20943","relation":"main_file","file_size":574389,"date_updated":"2026-01-05T12:16:38Z","access_level":"open_access","date_created":"2026-01-05T12:16:38Z","checksum":"1e05b4f17a44500ae1ae1e21bc636f6a","creator":"dernst","success":1}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"N. Zava, Algebraic &#38; Geometric Topology 25 (2025) 5153–5174.","ista":"Zava N. 2025. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces. Algebraic &#38; Geometric Topology. 25(8), 5153–5174.","apa":"Zava, N. (2025). Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces. <i>Algebraic &#38; Geometric Topology</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/agt.2025.25.5153\">https://doi.org/10.2140/agt.2025.25.5153</a>","mla":"Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the Gromov–Hausdorff Space into Hilbert Spaces.” <i>Algebraic &#38; Geometric Topology</i>, vol. 25, no. 8, Mathematical Sciences Publishers, 2025, pp. 5153–74, doi:<a href=\"https://doi.org/10.2140/agt.2025.25.5153\">10.2140/agt.2025.25.5153</a>.","chicago":"Zava, Nicolò. “Coarse and Bi-Lipschitz Embeddability of Subspaces of the Gromov–Hausdorff Space into Hilbert Spaces.” <i>Algebraic &#38; Geometric Topology</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/agt.2025.25.5153\">https://doi.org/10.2140/agt.2025.25.5153</a>.","ieee":"N. Zava, “Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces,” <i>Algebraic &#38; Geometric Topology</i>, vol. 25, no. 8. Mathematical Sciences Publishers, pp. 5153–5174, 2025.","ama":"Zava N. Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces. <i>Algebraic &#38; Geometric Topology</i>. 2025;25(8):5153-5174. doi:<a href=\"https://doi.org/10.2140/agt.2025.25.5153\">10.2140/agt.2025.25.5153</a>"},"date_published":"2025-11-20T00:00:00Z","intvolume":"        25","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"OA_place":"publisher","publisher":"Mathematical Sciences Publishers","language":[{"iso":"eng"}],"month":"11","publication":"Algebraic & Geometric Topology","quality_controlled":"1","article_processing_charge":"No","scopus_import":"1","publication_identifier":{"eissn":["1472-2739"],"issn":["1472-2747"]},"corr_author":"1","ddc":["500"],"title":"Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces","issue":"8","OA_type":"diamond","acknowledgement":"The author was supported by the FWF Grant, Project number I4245-N35. The author would like to thank Thomas Weighill for the helpful discussions around Theorem 3.10, and Takamitsu Yamauchi for bringing to my attention the fundamental reference [35]. Furthermore, the author\r\nis thankful for the detailed and helpful comments of the reviewer of this manuscript.","type":"journal_article","day":"20","status":"public","has_accepted_license":"1","date_created":"2025-12-29T12:09:09Z","arxiv":1,"doi":"10.2140/agt.2025.25.5153"},{"date_updated":"2025-09-09T13:23:12Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"publication_status":"published","year":"2023","volume":46,"oa_version":"None","_id":"14557","project":[{"call_identifier":"FWF","grant_number":"I04245","_id":"26AD5D90-B435-11E9-9278-68D0E5697425","name":"Algebraic Footprints of Geometric Features in Homology"}],"article_type":"original","page":"191-221","abstract":[{"text":"Motivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLattO of join semilattices with bottom element. In particular, we show that there are only finitely many closure operators of both categories, and provide a complete classification. We use this result to deduce the known fact that epimorphisms of SLatt and SLattO are surjective. We complement the paper with two different proofs of this result using either generators or Isbell’s zigzag theorem.","lang":"eng"}],"author":[{"last_name":"Dikranjan","first_name":"D.","full_name":"Dikranjan, D."},{"last_name":"Giordano Bruno","first_name":"A.","full_name":"Giordano Bruno, A."},{"first_name":"Nicolò","last_name":"Zava","orcid":"0000-0001-8686-1888","full_name":"Zava, Nicolò","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"}],"external_id":{"isi":["001098712000006"]},"department":[{"_id":"HeEd"}],"issue":"S1","title":"Epimorphisms and closure operators of categories of semilattices","scopus_import":"1","publication_identifier":{"issn":["1607-3606"],"eissn":["1727-933X"]},"doi":"10.2989/16073606.2023.2247731","date_created":"2023-11-19T23:00:55Z","status":"public","type":"journal_article","day":"01","acknowledgement":"The first and second named authors are members of GNSAGA – INdAM.\r\nThe third named author was supported by the FWF Grant, Project number I4245–N35","intvolume":"        46","date_published":"2023-11-01T00:00:00Z","citation":{"mla":"Dikranjan, D., et al. “Epimorphisms and Closure Operators of Categories of Semilattices.” <i>Quaestiones Mathematicae</i>, vol. 46, no. S1, Taylor &#38; Francis, 2023, pp. 191–221, doi:<a href=\"https://doi.org/10.2989/16073606.2023.2247731\">10.2989/16073606.2023.2247731</a>.","ieee":"D. Dikranjan, A. Giordano Bruno, and N. Zava, “Epimorphisms and closure operators of categories of semilattices,” <i>Quaestiones Mathematicae</i>, vol. 46, no. S1. Taylor &#38; Francis, pp. 191–221, 2023.","chicago":"Dikranjan, D., A. Giordano Bruno, and Nicolò Zava. “Epimorphisms and Closure Operators of Categories of Semilattices.” <i>Quaestiones Mathematicae</i>. Taylor &#38; Francis, 2023. <a href=\"https://doi.org/10.2989/16073606.2023.2247731\">https://doi.org/10.2989/16073606.2023.2247731</a>.","ama":"Dikranjan D, Giordano Bruno A, Zava N. Epimorphisms and closure operators of categories of semilattices. <i>Quaestiones Mathematicae</i>. 2023;46(S1):191-221. doi:<a href=\"https://doi.org/10.2989/16073606.2023.2247731\">10.2989/16073606.2023.2247731</a>","short":"D. Dikranjan, A. Giordano Bruno, N. Zava, Quaestiones Mathematicae 46 (2023) 191–221.","apa":"Dikranjan, D., Giordano Bruno, A., &#38; Zava, N. (2023). Epimorphisms and closure operators of categories of semilattices. <i>Quaestiones Mathematicae</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.2989/16073606.2023.2247731\">https://doi.org/10.2989/16073606.2023.2247731</a>","ista":"Dikranjan D, Giordano Bruno A, Zava N. 2023. Epimorphisms and closure operators of categories of semilattices. Quaestiones Mathematicae. 46(S1), 191–221."},"article_processing_charge":"No","quality_controlled":"1","publication":"Quaestiones Mathematicae","month":"11","language":[{"iso":"eng"}],"publisher":"Taylor & Francis"},{"date_updated":"2024-10-09T21:07:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"publication_status":"published","volume":977,"year":"2023","oa_version":"Preprint","_id":"14362","oa":1,"article_type":"original","abstract":[{"text":"Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwise weakly weighted (generalised) quasi-metrics. We then systematise and extend to full generality the correspondences between these objects and other structures arising in theoretical computer science and dynamics. In particular, we study the correspondences with weak partial metrics and, if the underlying space is a semilattice, with invariant (generalised) quasi-metrics satisfying the descending path condition, and with strictly monotone semi(-co-)valuations.\r\nWe conclude discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation of both the known intrinsic semilattice entropy and the semigroup entropy.","lang":"eng"}],"external_id":{"arxiv":["2212.08424"],"isi":["001076934000001"]},"author":[{"first_name":"Ilaria","last_name":"Castellano","full_name":"Castellano, Ilaria"},{"last_name":"Giordano Bruno","first_name":"Anna","full_name":"Giordano Bruno, Anna"},{"id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","orcid":"0000-0001-8686-1888","full_name":"Zava, Nicolò","last_name":"Zava","first_name":"Nicolò"}],"department":[{"_id":"HeEd"}],"title":"Weakly weighted generalised quasi-metric spaces and semilattices","scopus_import":"1","publication_identifier":{"issn":["0304-3975"]},"corr_author":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2212.08424 "}],"doi":"10.1016/j.tcs.2023.114129","arxiv":1,"date_created":"2023-09-24T22:01:11Z","status":"public","type":"journal_article","day":"25","article_number":"114129","intvolume":"       977","citation":{"mla":"Castellano, Ilaria, et al. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” <i>Theoretical Computer Science</i>, vol. 977, 114129, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.tcs.2023.114129\">10.1016/j.tcs.2023.114129</a>.","ama":"Castellano I, Giordano Bruno A, Zava N. Weakly weighted generalised quasi-metric spaces and semilattices. <i>Theoretical Computer Science</i>. 2023;977. doi:<a href=\"https://doi.org/10.1016/j.tcs.2023.114129\">10.1016/j.tcs.2023.114129</a>","ieee":"I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised quasi-metric spaces and semilattices,” <i>Theoretical Computer Science</i>, vol. 977. Elsevier, 2023.","chicago":"Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” <i>Theoretical Computer Science</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.tcs.2023.114129\">https://doi.org/10.1016/j.tcs.2023.114129</a>.","short":"I. Castellano, A. Giordano Bruno, N. Zava, Theoretical Computer Science 977 (2023).","ista":"Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129.","apa":"Castellano, I., Giordano Bruno, A., &#38; Zava, N. (2023). Weakly weighted generalised quasi-metric spaces and semilattices. <i>Theoretical Computer Science</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.tcs.2023.114129\">https://doi.org/10.1016/j.tcs.2023.114129</a>"},"date_published":"2023-10-25T00:00:00Z","quality_controlled":"1","article_processing_charge":"No","publication":"Theoretical Computer Science","month":"10","publisher":"Elsevier","language":[{"iso":"eng"}]},{"publication":"Topology and its Applications","quality_controlled":"1","article_processing_charge":"No","publisher":"Elsevier","language":[{"iso":"eng"}],"month":"03","intvolume":"       309","article_number":"107916","citation":{"short":"D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology and Its Applications 309 (2022).","ista":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized quasi-metric semilattices. Topology and its Applications. 309, 107916.","apa":"Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., &#38; Toller, D. (2022). Generalized quasi-metric semilattices. <i>Topology and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.topol.2021.107916\">https://doi.org/10.1016/j.topol.2021.107916</a>","mla":"Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” <i>Topology and Its Applications</i>, vol. 309, 107916, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.topol.2021.107916\">10.1016/j.topol.2021.107916</a>.","ama":"Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric semilattices. <i>Topology and its Applications</i>. 2022;309. doi:<a href=\"https://doi.org/10.1016/j.topol.2021.107916\">10.1016/j.topol.2021.107916</a>","chicago":"Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava, and Daniele Toller. “Generalized Quasi-Metric Semilattices.” <i>Topology and Its Applications</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.topol.2021.107916\">https://doi.org/10.1016/j.topol.2021.107916</a>.","ieee":"D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized quasi-metric semilattices,” <i>Topology and its Applications</i>, vol. 309. Elsevier, 2022."},"date_published":"2022-03-15T00:00:00Z","status":"public","date_created":"2021-12-05T23:01:44Z","doi":"10.1016/j.topol.2021.107916","acknowledgement":"Dedicated to the memory of Hans-Peter Künzi.","type":"journal_article","day":"15","title":"Generalized quasi-metric semilattices","scopus_import":"1","publication_identifier":{"issn":["0166-8641"]},"corr_author":"1","external_id":{"isi":["000791838800012"]},"author":[{"first_name":"Dikran","last_name":"Dikranjan","full_name":"Dikranjan, Dikran"},{"first_name":"Anna","last_name":"Giordano Bruno","full_name":"Giordano Bruno, Anna"},{"full_name":"Künzi, Hans Peter","first_name":"Hans Peter","last_name":"Künzi"},{"first_name":"Nicolò","last_name":"Zava","full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888","id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad"},{"full_name":"Toller, Daniele","last_name":"Toller","first_name":"Daniele"}],"abstract":[{"text":"Motivated by the recent introduction of the intrinsic semilattice entropy, we study generalized quasi-metric semilattices and their categories. We investigate the relationship between these objects and generalized semivaluations, extending Nakamura and Schellekens' approach. Finally, we use this correspondence to compare the intrinsic semilattice entropy and the semigroup entropy induced in particular situations, like sets, torsion abelian groups and vector spaces.","lang":"eng"}],"department":[{"_id":"HeEd"}],"_id":"10413","oa_version":"None","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"volume":309,"year":"2022","publication_status":"published","date_updated":"2024-10-09T21:01:16Z"},{"publication":"European Journal of Mathematics","article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","language":[{"iso":"eng"}],"publisher":"Springer Nature","month":"03","intvolume":"         8","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2022-03-01T00:00:00Z","citation":{"mla":"Weighill, Thomas, et al. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” <i>European Journal of Mathematics</i>, vol. 8, no. 1, Springer Nature, 2022, pp. 335–55, doi:<a href=\"https://doi.org/10.1007/s40879-021-00515-3\">10.1007/s40879-021-00515-3</a>.","ieee":"T. Weighill, T. Yamauchi, and N. Zava, “Coarse infinite-dimensionality of hyperspaces of finite subsets,” <i>European Journal of Mathematics</i>, vol. 8, no. 1. Springer Nature, pp. 335–355, 2022.","chicago":"Weighill, Thomas, Takamitsu Yamauchi, and Nicolò Zava. “Coarse Infinite-Dimensionality of Hyperspaces of Finite Subsets.” <i>European Journal of Mathematics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40879-021-00515-3\">https://doi.org/10.1007/s40879-021-00515-3</a>.","ama":"Weighill T, Yamauchi T, Zava N. Coarse infinite-dimensionality of hyperspaces of finite subsets. <i>European Journal of Mathematics</i>. 2022;8(1):335-355. doi:<a href=\"https://doi.org/10.1007/s40879-021-00515-3\">10.1007/s40879-021-00515-3</a>","short":"T. Weighill, T. Yamauchi, N. Zava, European Journal of Mathematics 8 (2022) 335–355.","ista":"Weighill T, Yamauchi T, Zava N. 2022. Coarse infinite-dimensionality of hyperspaces of finite subsets. European Journal of Mathematics. 8(1), 335–355.","apa":"Weighill, T., Yamauchi, T., &#38; Zava, N. (2022). Coarse infinite-dimensionality of hyperspaces of finite subsets. <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-021-00515-3\">https://doi.org/10.1007/s40879-021-00515-3</a>"},"status":"public","has_accepted_license":"1","doi":"10.1007/s40879-021-00515-3","date_created":"2022-01-09T23:01:27Z","acknowledgement":"We would like to thank the referees for their careful reading and the comments that improved our work. The third named author would like to thank the Division of Mathematics, Physics and Earth Sciences of the Graduate School of Science and Engineering of Ehime University and the second named author for hosting his visit in June 2018. Open access funding provided by Institute of Science and Technology (IST Austria).","type":"journal_article","day":"01","issue":"1","title":"Coarse infinite-dimensionality of hyperspaces of finite subsets","ddc":["500"],"publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"scopus_import":"1","author":[{"full_name":"Weighill, Thomas","first_name":"Thomas","last_name":"Weighill"},{"full_name":"Yamauchi, Takamitsu","first_name":"Takamitsu","last_name":"Yamauchi"},{"id":"c8b3499c-7a77-11eb-b046-aa368cbbf2ad","full_name":"Zava, Nicolò","orcid":"0000-0001-8686-1888","last_name":"Zava","first_name":"Nicolò"}],"abstract":[{"lang":"eng","text":"We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property."}],"department":[{"_id":"HeEd"}],"_id":"10608","oa_version":"Published Version","page":"335-355","article_type":"original","oa":1,"file":[{"checksum":"ce35cbb2d8c889dc7750719972634ed4","date_created":"2024-05-22T11:10:10Z","success":1,"creator":"kschuh","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"17036","file_size":371515,"date_updated":"2024-05-22T11:10:10Z","file_name":"2022_EuJournalMath_Weighill.pdf"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2022","volume":8,"publication_status":"published","date_updated":"2024-05-22T11:10:22Z","file_date_updated":"2024-05-22T11:10:10Z"}]