On a new convergence in topological spaces
In this paper, we introduce a new way-below relation in T0 topological spaces based on cuts and give the concepts of SI2-continuous spaces and weakly irreducible topologies. It is proved that a space is SI2-continuous if and only if its weakly irreducible topology is completely distributive under in...
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-12-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2019-0123 |
| _version_ | 1818716602724515840 |
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| author | Ruan Xiao-jun Xu Xiao-quan |
| author_facet | Ruan Xiao-jun Xu Xiao-quan |
| author_sort | Ruan Xiao-jun |
| collection | DOAJ |
| description | In this paper, we introduce a new way-below relation in T0 topological spaces based on cuts and give the concepts of SI2-continuous spaces and weakly irreducible topologies. It is proved that a space is SI2-continuous if and only if its weakly irreducible topology is completely distributive under inclusion order. Finally, we introduce the concept of 𝓓-convergence and show that a space is SI2-continuous if and only if its 𝓓-convergence with respect to the topology τSI2(X) is topological. In general, a space is SI-continuous if and only if its 𝓓-convergence with respect to the topology τSI(X) is topological. |
| first_indexed | 2024-12-17T19:21:52Z |
| format | Article |
| id | doaj.art-d72e70f827cb45cbb8aba43d0a084505 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T19:21:52Z |
| publishDate | 2019-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-d72e70f827cb45cbb8aba43d0a0845052022-12-21T21:35:29ZengDe GruyterOpen Mathematics2391-54552019-12-011711716172310.1515/math-2019-0123math-2019-0123On a new convergence in topological spacesRuan Xiao-jun0Xu Xiao-quan1Department of Mathematics, Nanchang University, Nanchang, 330031, ChinaSchool of Mathematics and Statistics, Minnan Normal University, Zhangzhou, 363000, ChinaIn this paper, we introduce a new way-below relation in T0 topological spaces based on cuts and give the concepts of SI2-continuous spaces and weakly irreducible topologies. It is proved that a space is SI2-continuous if and only if its weakly irreducible topology is completely distributive under inclusion order. Finally, we introduce the concept of 𝓓-convergence and show that a space is SI2-continuous if and only if its 𝓓-convergence with respect to the topology τSI2(X) is topological. In general, a space is SI-continuous if and only if its 𝓓-convergence with respect to the topology τSI(X) is topological.https://doi.org/10.1515/math-2019-0123s2-continuous posetweakly irreducible topologysi2-continuous space𝓓-convergence06b3506b7554f05 |
| spellingShingle | Ruan Xiao-jun Xu Xiao-quan On a new convergence in topological spaces Open Mathematics s2-continuous poset weakly irreducible topology si2-continuous space 𝓓-convergence 06b35 06b75 54f05 |
| title | On a new convergence in topological spaces |
| title_full | On a new convergence in topological spaces |
| title_fullStr | On a new convergence in topological spaces |
| title_full_unstemmed | On a new convergence in topological spaces |
| title_short | On a new convergence in topological spaces |
| title_sort | on a new convergence in topological spaces |
| topic | s2-continuous poset weakly irreducible topology si2-continuous space 𝓓-convergence 06b35 06b75 54f05 |
| url | https://doi.org/10.1515/math-2019-0123 |
| work_keys_str_mv | AT ruanxiaojun onanewconvergenceintopologicalspaces AT xuxiaoquan onanewconvergenceintopologicalspaces |