Z-continuous and Z-Scott completion of topological space(拓扑空间的Z连续性与Z-Scott完备化)
The concepts of Z-continuous spaces and Z-bases are introduced, and the Z-Scott completion of topological spaces is studied. The main conclusions are: (1) The T0 topological space X is a Z-continuous space if and only if X has a Z-basis; (2) The Z-closed subspace of Z-continuous space is Z-continuou...
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2025-07-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2025.04.005 |
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| author | 张舜(ZHANG Shun) 王武(WANG Wu) |
| author_facet | 张舜(ZHANG Shun) 王武(WANG Wu) |
| author_sort | 张舜(ZHANG Shun) |
| collection | DOAJ |
| description | The concepts of Z-continuous spaces and Z-bases are introduced, and the Z-Scott completion of topological spaces is studied. The main conclusions are: (1) The T0 topological space X is a Z-continuous space if and only if X has a Z-basis; (2) The Z-closed subspace of Z-continuous space is Z-continuous; (3) Z-Scott completion exists in any T0 topological space exists.引入了Z连续空间和Z基概念，研究了拓扑空间的Z-Scott完备化。主要结论有：（1）T0拓扑空间X是Z连续空间当且仅当X有Z基；（2）Z连续空间的Z闭子空间是Z连续的；（3）任意T0拓扑空间存在Z-Scott完备化。 |
| format | Article |
| id | doaj-art-dee34a234ce14359ad2e135ef951bf82 |
| institution | Kabale University |
| issn | 1008-9497 |
| language | zho |
| publishDate | 2025-07-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj-art-dee34a234ce14359ad2e135ef951bf822025-08-20T04:02:27ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972025-07-0152445946310.3785/j.issn.1008-9497.2025.04.005Z-continuous and Z-Scott completion of topological space(拓扑空间的Z连续性与Z-Scott完备化)张舜(ZHANG Shun)0https://orcid.org/0000-0001-9001-9394王武(WANG Wu)1https://orcid.org/0000-0002-5824-40891Tianjin Renai College， Tianjin 301636， China(1天津仁爱学院，天津 301636)2Zhonghuan Information College， Tianjin University of Technology， Tianjin 300380， China(2天津理工大学 中环信息学院，天津 300380)The concepts of Z-continuous spaces and Z-bases are introduced, and the Z-Scott completion of topological spaces is studied. The main conclusions are: (1) The T0 topological space X is a Z-continuous space if and only if X has a Z-basis; (2) The Z-closed subspace of Z-continuous space is Z-continuous; (3) Z-Scott completion exists in any T0 topological space exists.引入了Z连续空间和Z基概念，研究了拓扑空间的Z-Scott完备化。主要结论有：（1）T0拓扑空间X是Z连续空间当且仅当X有Z基；（2）Z连续空间的Z闭子空间是Z连续的；（3）任意T0拓扑空间存在Z-Scott完备化。https://doi.org/10.3785/j.issn.1008-9497.2025.04.005 |
| spellingShingle | 张舜(ZHANG Shun) 王武(WANG Wu) Z-continuous and Z-Scott completion of topological space(拓扑空间的Z连续性与Z-Scott完备化) Zhejiang Daxue xuebao. Lixue ban |
| title | Z-continuous and Z-Scott completion of topological space(拓扑空间的Z连续性与Z-Scott完备化) |
| title_full | Z-continuous and Z-Scott completion of topological space(拓扑空间的Z连续性与Z-Scott完备化) |
| title_fullStr | Z-continuous and Z-Scott completion of topological space(拓扑空间的Z连续性与Z-Scott完备化) |
| title_full_unstemmed | Z-continuous and Z-Scott completion of topological space(拓扑空间的Z连续性与Z-Scott完备化) |
| title_short | Z-continuous and Z-Scott completion of topological space(拓扑空间的Z连续性与Z-Scott完备化) |
| title_sort | z continuous and z scott completion of topological space 拓扑空间的z连续性与z scott完备化 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2025.04.005 |
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