Title
A note on the hyperspace of finite subsets
Authors
Year of publication
2021
Published in
Article type
scientific article
Publication language
english
Keywords
EN
- symmetric product
- hyperspace
- sp-network
- stric B0-space
- P-space
- sequentially separable
Abstract
EN In this paper, we study the relation between a space X satisfying certain generalized metric properties and its hyperspace of finite subsets F(X) satisfying the same properties. We prove that if F(X) is a stric B0-space then so is X. However, there exists a stric B0-space X such that Fn(X) is not a stric B0-space for each n ≥ 2, hence F(X) is not a stric B0-space. Moreover, we prove that X is a P -space (resp., sequentially separable) if and only if so is F(X).
Pages (from - to)
67 - 73
Full text of article
Access level to full text
public
Ministry points / journal
5
Ministry points / journal in years 2017-2021
5
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