Weakly weighted generalised quasi-metric spaces and semilattices
Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129.
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https://doi.org/10.48550/arXiv.2212.08424
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Journal Article
| Published
| English
Scopus indexed
Author
Castellano, Ilaria;
Giordano Bruno, Anna;
Zava, NicolòISTA
Department
Abstract
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.
We conclude discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation of both the known intrinsic semilattice entropy and the semigroup entropy.
Publishing Year
Date Published
2023-10-25
Journal Title
Theoretical Computer Science
Volume
977
Article Number
114129
ISSN
IST-REx-ID
Cite this
Castellano I, Giordano Bruno A, Zava N. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 2023;977. doi:10.1016/j.tcs.2023.114129
Castellano, I., Giordano Bruno, A., & Zava, N. (2023). Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. Elsevier. https://doi.org/10.1016/j.tcs.2023.114129
Castellano, Ilaria, Anna Giordano Bruno, and Nicolò Zava. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science. Elsevier, 2023. https://doi.org/10.1016/j.tcs.2023.114129.
I. Castellano, A. Giordano Bruno, and N. Zava, “Weakly weighted generalised quasi-metric spaces and semilattices,” Theoretical Computer Science, vol. 977. Elsevier, 2023.
Castellano I, Giordano Bruno A, Zava N. 2023. Weakly weighted generalised quasi-metric spaces and semilattices. Theoretical Computer Science. 977, 114129.
Castellano, Ilaria, et al. “Weakly Weighted Generalised Quasi-Metric Spaces and Semilattices.” Theoretical Computer Science, vol. 977, 114129, Elsevier, 2023, doi:10.1016/j.tcs.2023.114129.
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arXiv 2212.08424