arXiv:1801.05633 Abstract | arXiv Analytics

arXiv:1801.05633 [math.GN]Abstract References Reviews Resources

The Baire category of the hyperspace of nontrivial convergent sequences

Published 2018-01-17Version 1

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.

Categories: math.GN

Subjects: 54B20, 54E52, 54A20

Keywords: nontrivial convergent sequences, baire category, hyperspace, regular space, study topological properties

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