典范超连通空间的尺度及其Vietoris超空间

中文摘要 AI 辅助

对于无限基数$\lambda \leq \kappa$，我们计算了基数为$\kappa$的拓扑空间$X$的尺度，其中$X$的开集是满足$|X \setminus A| < \lambda$的子集$A$。我们还证明了$X$的尺度集合与Vietoris超空间$\mathcal{H}(X)$的尺度集合一致，其中$\mathcal{H}(X)$的底集是$X$的子集族，该族包含$X$的所有有限子集，并且包含于$X$的闭子集族中。

英文摘要

For infinite cardinals $λ\leq κ$, we calculate the calibers of topological spaces $X$ of cardinality $κ$ whose open sets are the subsets $A$ satisfying $|X \setminus A| < λ$. We also prove that the set of calibers of $X$ coincides with the set of calibers of the Vietoris hyperspace $\mathcal{H}(X)$, where the space $\mathcal{H}(X)$ 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.

发表机构

• Universidad Nacional Autónoma de México（墨西哥国立自治大学）

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