Coarse infinite-dimensionality of hyperspaces of finite subsets
Weighill, Thomas
Yamauchi, Takamitsu
Zava, NicolĂ˛
ddc:500
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.
Springer Nature
2022
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.ista.ac.at/record/10608
https://research-explorer.ista.ac.at/download/10608/17036
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>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1007/s40879-021-00515-3
info:eu-repo/semantics/altIdentifier/issn/2199-675X
info:eu-repo/semantics/altIdentifier/issn/2199-6768
https://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess