非平凡收敛序列的超空间的贝尔范畴

Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021 Pub Date : 2018-01-17 DOI:10.2478/9788366675360-018

M. Poplawski

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引用次数: 0

摘要

假设$X$是一个正则空间。研究了具有Vietoris拓扑的$X$上的非平凡收敛序列$S_c(X)$族的拓扑性质。我们证明了如果$X$没有孤立点，则$S_c(X)$是第一类空间，它回答了S. Garcia-Ferreira和Y.F. Ortiz-Castillo提出的问题。

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THE BAIRE CATEGORY OF THE HYPERSPACE OF NONTRIVIAL CONVERGENT SEQUENCES

Assume that $X$ is a regular space. We study topological properties of the family $S_c(X)$ of nontrivial convergent sequences in $X$ equipped with the Vietoris topology. We show that if $X$ has no isolated points, then $S_c(X)$ is a space of the first category which answers the question posed by S. Garcia-Ferreira and Y.F. Ortiz-Castillo.

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Proceedings of the conference Contemporary Mathematics in Kielce 2020, February 24-27 2021

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