$\omega$ -cover and related spaces on the vietoris hyperspace $\mathcal F(X)$
Recently, Tuyen et al. [1] showed that a space has a $\sigma$-(P)-strong network consisting of cs-covers (resp., $cs^*$-covers) if and only if the hyperspace $\mathcal F(X)$ does, where is one of the following properties: point finite, point countable, compact finite, compact-countable, locally fi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
The University of Danang
2024-12-01
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| Series: | Tạp chí Khoa học và Công nghệ |
| Subjects: | |
| Online Access: | https://jst-ud.vn/jst-ud/article/view/9465 |
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| Summary: | Recently, Tuyen et al. [1] showed that a space has a $\sigma$-(P)-strong network consisting of cs-covers (resp., $cs^*$-covers) if and only if the hyperspace $\mathcal F(X)$ does, where is one of the following properties: point finite, point countable, compact finite, compact-countable, locally finite, locally countable. Moreover, they we also proved that is a Cauchy sn-symmetric space with a $\sigma$-(P)-property $cs^*$-network (resp., cs-network, sn-network.) if and only if so is $\mathcal F(X)$ (see [1]). In this paper, we study the concepts of $\omega$-cover and certain spaces defined by $\omega$-covers on the hyperspace of finite subsets of a space X endowed with the Vietoris topology. We prove that is an $\omega$-Lindelöf (resp., $\omega$-Menger, $\omega$-Rothberger) space if and only if so is $\mathcal F(X)$. |
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| ISSN: | 1859-1531 |