Co-Noetherian spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866914258638340096 |
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| author | Li, Xiangrui Li, Qingguo |
| author_facet | Li, Xiangrui Li, Qingguo |
| contents | In non-Hausdorff topology, many spaces exhibit significant separation properties, such as sober spaces, well-filtered spaces and d-spaces. These properties serve to fundamentally classify T0 topological spaces. In this paper, we introduce and study a new class of topological spaces called co-Noetherian spaces, which can refine the classification of T0 spaces. We discuss some basic properties of co-Noetherian spaces and obtain an equivalent characterization of compactness under the strong topology. Additionally, we investigate the connections among KC-spaces, strong R-spaces and co-Noetherian spaces. Moreover, we establish an equivalence between the category of T0 co-Noetherian spaces with continuous mappings and a subcategory of the poset category. Finally, we provide counterexamples to show that the Hoare powerspace of a T0 space may fail to be co-Noetherian, and that the Smyth powerspace of a co-Noetherian space need not be co-Noetherian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11112 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Co-Noetherian spaces Li, Xiangrui Li, Qingguo General Topology 54D10, 54B20, 06B35, 06F30 In non-Hausdorff topology, many spaces exhibit significant separation properties, such as sober spaces, well-filtered spaces and d-spaces. These properties serve to fundamentally classify T0 topological spaces. In this paper, we introduce and study a new class of topological spaces called co-Noetherian spaces, which can refine the classification of T0 spaces. We discuss some basic properties of co-Noetherian spaces and obtain an equivalent characterization of compactness under the strong topology. Additionally, we investigate the connections among KC-spaces, strong R-spaces and co-Noetherian spaces. Moreover, we establish an equivalence between the category of T0 co-Noetherian spaces with continuous mappings and a subcategory of the poset category. Finally, we provide counterexamples to show that the Hoare powerspace of a T0 space may fail to be co-Noetherian, and that the Smyth powerspace of a co-Noetherian space need not be co-Noetherian. |
| title | Co-Noetherian spaces |
| topic | General Topology 54D10, 54B20, 06B35, 06F30 |
| url | https://arxiv.org/abs/2601.11112 |