Strong well-filteredness of upper topology on sup-complete posets
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915669293924352 |
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| author | Xu, Xiaoquan Yang, Yi Chen, Lizi |
| author_facet | Xu, Xiaoquan Yang, Yi Chen, Lizi |
| contents | We first introduce and investigate a new class of $T_0$ spaces -- strong R-spaces, which are stronger than both R-spaces and strongly well-filtered spaces. It is proved that any sup-complete poset equipped with the upper topology is a strong R-space and the Hoare power space of a $T_0$-space is a strong R-space. Hence the upper topology on a sup-complete poset is strongly well-filtered and the Hoare power space of a $T_0$-space is strongly well-filtered, which answers two problems recently posed by Xu. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong well-filteredness of upper topology on sup-complete posets Xu, Xiaoquan Yang, Yi Chen, Lizi General Topology 54D10, 54B20, 06B35, 06F30 We first introduce and investigate a new class of $T_0$ spaces -- strong R-spaces, which are stronger than both R-spaces and strongly well-filtered spaces. It is proved that any sup-complete poset equipped with the upper topology is a strong R-space and the Hoare power space of a $T_0$-space is a strong R-space. Hence the upper topology on a sup-complete poset is strongly well-filtered and the Hoare power space of a $T_0$-space is strongly well-filtered, which answers two problems recently posed by Xu. |
| title | Strong well-filteredness of upper topology on sup-complete posets |
| topic | General Topology 54D10, 54B20, 06B35, 06F30 |
| url | https://arxiv.org/abs/2512.10599 |