Year: 2026
Type: preprint
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 $\mathcal{H}(X)$ lying between $\mathrm{CL}(X)$ and $\mathcal{F}(X)$. For infinite metrizable spaces, we characterize several cases in which $\mathsf{SC}(X)$ and $\mathsf{SC}(\mathrm{CL}(X))$ differ and establish an independence result over \textsf{ZFC}; see Theorem~5.12.
Source: arXiv (Cornell University)
Author: Ríos-Herrejón, Alejandro
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214039401