$\omega$ -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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| Language: | English |
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The University of Danang
2024-12-01
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| Series: | Tạp chí Khoa học và Công nghệ |
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| Online Access: | https://jst-ud.vn/jst-ud/article/view/9465 |
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| author | Nguyen Xuan Truc Nguyen Thi Hong Phuc Ong Van Tuyen Luong Quoc Tuyen |
| author_facet | Nguyen Xuan Truc Nguyen Thi Hong Phuc Ong Van Tuyen Luong Quoc Tuyen |
| author_sort | Nguyen Xuan Truc |
| collection | DOAJ |
| description | 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 $\mathcal F(X)$. |
| format | Article |
| id | doaj-art-3217483902e84b7f9bcd67baa39565d8 |
| institution | OA Journals |
| issn | 1859-1531 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | The University of Danang |
| record_format | Article |
| series | Tạp chí Khoa học và Công nghệ |
| spelling | doaj-art-3217483902e84b7f9bcd67baa39565d82025-08-20T02:14:32ZengThe University of DanangTạp chí Khoa học và Công nghệ1859-15312024-12-01838710.31130/ud-jst.2024.458E9459$\omega$ -cover and related spaces on the vietoris hyperspace $\mathcal F(X)$Nguyen Xuan Truc0Nguyen Thi Hong Phuc1Ong Van Tuyen2Luong Quoc Tuyen3Students of Mathematics, The University of Danang - University of Science and Education, VietnamStudents of Mathematics, The University of Danang - University of Science and Education, VietnamHoa Vang High School, Da Nang, VietnamThe University of Danang - University of Science and Education, VietnamRecently, 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 $\mathcal F(X)$.https://jst-ud.vn/jst-ud/article/view/9465$\omega$-covervietoris hyperspace$\omega$-lindelöf$\omega$-menger$\omega$-rothberger |
| spellingShingle | Nguyen Xuan Truc Nguyen Thi Hong Phuc Ong Van Tuyen Luong Quoc Tuyen $\omega$ -cover and related spaces on the vietoris hyperspace $\mathcal F(X)$ Tạp chí Khoa học và Công nghệ $\omega$-cover vietoris hyperspace $\omega$-lindelöf $\omega$-menger $\omega$-rothberger |
| title | $\omega$ -cover and related spaces on the vietoris hyperspace $\mathcal F(X)$ |
| title_full | $\omega$ -cover and related spaces on the vietoris hyperspace $\mathcal F(X)$ |
| title_fullStr | $\omega$ -cover and related spaces on the vietoris hyperspace $\mathcal F(X)$ |
| title_full_unstemmed | $\omega$ -cover and related spaces on the vietoris hyperspace $\mathcal F(X)$ |
| title_short | $\omega$ -cover and related spaces on the vietoris hyperspace $\mathcal F(X)$ |
| title_sort | omega cover and related spaces on the vietoris hyperspace mathcal f x |
| topic | $\omega$-cover vietoris hyperspace $\omega$-lindelöf $\omega$-menger $\omega$-rothberger |
| url | https://jst-ud.vn/jst-ud/article/view/9465 |
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