Article
| Title: | About $wcs$-covers and $wcs^*$-networks on the Vietoris hyperspace $\mathcal F(X)$ (English) |
| Author: | Tuyen, Luong Q. |
| Author: | Tuyen, Ong V. |
| Author: | Tuan, Phan D. |
| Author: | Truc, Nguzen X. |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 519-527 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study some generalized metric properties on the hyperspace $\mathcal F(X)$ of finite subsets of a space $X$ endowed with the Vietoris topology. We prove that $X$ has a point-star network consisting of (countable) $wcs$-covers if and only if so does $\mathcal F(X)$. Moreover, $X$ has a sequence of $wcs$-covers with property $(P)$ which is a point-star network if and only if so does $\mathcal F(X)$, where $(P)$ is one of the following properties: point-finite, point-countable, compact-finite, compact-countable, locally finite, locally countable. On the other hand, $X$ has a $wcs^*$-network with property $\sigma$-$(P)$ if and only if so does $\mathcal F(X)$. By these results, we obtain some results related to the images of metric spaces and separable metric spaces under some kinds of continuous mappings on the Vietoris hyperspace $\mathcal F(X)$. (English) |
| Keyword: | hyperspace |
| Keyword: | generalized metric property |
| Keyword: | $wcs$-cover |
| Keyword: | $wcs^*$-network |
| MSC: | 54B20 |
| MSC: | 54C10 |
| MSC: | 54D20 |
| MSC: | 54E40 |
| DOI: | 10.14712/1213-7243.2024.011 |
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| Date available: | 2024-11-05T11:54:58Z |
| Last updated: | 2024-11-05 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152619 |
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