PreprintCC BY-NC-SA 4.0arXiv
Super calibers in topological spaces and topological hyperspaces
Abstract
We study the notion of a super caliber of a topological space, which is closely related to the classical notion of caliber and has appeared in the literature under several different names. We collect and unify several known results and establish new results concerning the collections of super calibers of topological spaces and their hyperspaces. In particular, we investigate the relationship between the super calibers of a space X and those of hyperspaces ℋ(X) lying between CL(X) and ℱ(X). For infinite metrizable spaces, we characterize several cases in which SC(X) and SC(CL(X)) differ and establish an independence result over \textsf{ZFC}; see Theorem~5.12.
Related
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BibTeX
@misc{riosherrejon2026super,
title = {{Super calibers in topological spaces and topological hyperspaces}},
author = {Alejandro Ríos-Herrejón},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23335},
eprint = {2609.23335},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23335},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Super calibers in topological spaces and topological hyperspaces
AU - Alejandro Ríos-Herrejón
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23335
UR - https://arxiv.org/abs/2609.23335
AB - We study the notion of a super caliber of a topological space, which is closely related to the classical notion of caliber and has appeared in the literature under several different names. We collect and unify several known results and establish new results concerning the collections of super calibers of topological spaces and their hyperspaces. In particular, we investigate the relationship between the super calibers of a space X and those of hyperspaces ℋ(X) lying between CL(X) and ℱ(X). For infinite metrizable spaces, we characterize several cases in which SC(X) and SC(CL(X)) differ and establish an independence result over \textsf{ZFC}; see Theorem~5.12.
ER -