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arXiv · 1801.05633

The Baire category of the hyperspace of nontrivial convergent sequences

Michał Popławski
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Abstract

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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Michał Popławski. 2018-01-17. The Baire category of the hyperspace of nontrivial convergent sequences. https://arxiv.org/abs/1801.05633

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