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arXiv · 1911.12940

Some generalized metric properties on hyperspaces with the Vietoris topology

Fucai Lin·Rongxin Shen·Chuan Liu
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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.

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Fucai Lin, Rongxin Shen, Chuan Liu. 2019-11-29. Some generalized metric properties on hyperspaces with the Vietoris topology. https://arxiv.org/abs/1911.12940

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