Some generalized metric properties on hyperspaces with the Vietoris topology

2019/11/29 by Fucai Lin, Rongxin Shen, Lin, Fucai +3 · 1 citation
Decision Sciences · Mathematics · #54B20 #54D20 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.1911.12940

openalex publication_date 2019/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the heredity of the classes of generalized metric spaces (for example, spaces with a σ-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, γ-spaces, semi-metrizable spaces) to the hyperspaces of nonempty compact subsets and finite subsets with the Vietoris topology.

Citations

• Fans and their applications in General Topology, Functional Analysis and Topological Algebra

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• Hyperspace of finite unions of convergent sequences

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