Some generalized metric properties on hyperspaces with the Vietoris topology

Fucai Lin; Rongxin Shen; Chuan Liu

Some generalized metric properties on hyperspaces with the Vietoris topology

General Topology 2019-12-02 v1

Authors: Fucai Lin , Rongxin Shen , Chuan Liu

Abstract

We study the heredity of the classes of generalized metric spaces (for example, spaces with a $\sigma$ -hereditarily closure-preserving $k$ -network, spaces with a point-countable base, spaces with a base of countable order, spaces with a point-regular base, Nagata-spaces, $c$ -semi-stratifiable spaces, $\gamma$ -spaces, semi-metrizable spaces) to the hyperspaces of nonempty compact subsets and finite subsets with the Vietoris topology.

Keywords

generalized metric spaces hyperspaces vietoris topology heredity compact subsets finite subsets k-network

Cite

@article{arxiv.1911.12940,
  title  = {Some generalized metric properties on hyperspaces with the Vietoris topology},
  author = {Fucai Lin and Rongxin Shen and Chuan Liu},
  journal= {arXiv preprint arXiv:1911.12940},
  year   = {2019}
}

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Some generalized metric properties on hyperspaces with the Vietoris topology

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