PreprintCC BY-NC-SA 4.0arXiv
Calibers of canonical hyperconnected spaces and their Vietoris hyperspaces
Abstract
For infinite cardinals λ≤ κ, we calculate the calibers of topological spaces X of cardinality κ whose open sets are the subsets A satisfying |X ∖ A| < λ. We also prove that the set of calibers of X coincides with the set of calibers of the Vietoris hyperspace ℋ(X), where the space ℋ(X) has as its underlying set a collection of subsets of X that includes all its finite subsets and is contained within the collection of its closed subsets.
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BibTeX
@misc{riosherrejon2026calibers,
title = {{Calibers of canonical hyperconnected spaces and their Vietoris hyperspaces}},
author = {Alejandro Ríos-Herrejón and Ángel Tamariz-Mascarúa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22679},
eprint = {2609.22679},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22679},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Calibers of canonical hyperconnected spaces and their Vietoris hyperspaces
AU - Alejandro Ríos-Herrejón
AU - Ángel Tamariz-Mascarúa
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22679
UR - https://arxiv.org/abs/2609.22679
AB - For infinite cardinals λ≤ κ, we calculate the calibers of topological spaces X of cardinality κ whose open sets are the subsets A satisfying |X ∖ A| < λ. We also prove that the set of calibers of X coincides with the set of calibers of the Vietoris hyperspace ℋ(X), where the space ℋ(X) has as its underlying set a collection of subsets of X that includes all its finite subsets and is contained within the collection of its closed subsets.
ER -