发表机构
Universidad Nacional Autónoma de México（墨西哥国立自治大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究拓扑空间及其超空间的超口径概念，统一已知结果，刻画无限可度量化空间中超口径差异情形，并证明一个ZFC独立性结果。
AI 中文摘要
我们研究了拓扑空间的超口径概念，该概念与经典的口径概念密切相关，并在文献中以多种不同名称出现。我们收集并统一了若干已知结果，并建立了关于拓扑空间及其超空间的超口径族的新结果。特别地，我们研究了空间$X$的超口径与位于$\mathrm{CL}(X)$和$\mathcal{F}(X)$之间的超空间$\mathcal{H}(X)$的超口径之间的关系。对于无限可度量化空间，我们刻画了$\mathsf{SC}(X)$与$\mathsf{SC}(\mathrm{CL}(X))$不同的若干情形，并在\textsf{ZFC}上建立了一个独立性结果；参见定理5.12。
英文摘要
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.
