S*-well-filtered spaces and d*-spaces
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| Format: | Preprint |
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2026
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| _version_ | 1866917206551429120 |
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| author | Han, Nana Chen, Siheng Li, Qingguo |
| author_facet | Han, Nana Chen, Siheng Li, Qingguo |
| contents | Recently, Xu proposed a strongly well-filtered space in [24] and systematically investigated some of its properties and characterizations. In this paper, we introduce a new class of T0-spaces called S*-well-filtered spaces, which is strictly larger than the class of strongly well-filtered spaces. First, we establish some connections among S*-well-filtered spaces, d*-spaces and weak well-filtered spaces. Then it is demonstrated that for any dcpo P, the Scott space ΣP is a d*-space if and only if it is S*-well-filtered. Furthermore, some basic properties of S*-well-filtered spaces are discussed. We prove that if Y is an S*-well-filtered space, the function space TOP(X,Y) equipped with the Isbell topology may not be an S*-well-filtered space. Finally, we study the S*-well-filteredness of Smyth power spaces. In addition, Johnstone's non-sober dcpo example is shown to be S*-well-filtered yet it is not strongly well-filtered, thereby establishing an obvious distinction between these two classes of dcpos. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_11281 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | S*-well-filtered spaces and d*-spaces Han, Nana Chen, Siheng Li, Qingguo General Topology 06 Order, lattices, order algebraic structures, 54 General topology Recently, Xu proposed a strongly well-filtered space in [24] and systematically investigated some of its properties and characterizations. In this paper, we introduce a new class of T0-spaces called S*-well-filtered spaces, which is strictly larger than the class of strongly well-filtered spaces. First, we establish some connections among S*-well-filtered spaces, d*-spaces and weak well-filtered spaces. Then it is demonstrated that for any dcpo P, the Scott space ΣP is a d*-space if and only if it is S*-well-filtered. Furthermore, some basic properties of S*-well-filtered spaces are discussed. We prove that if Y is an S*-well-filtered space, the function space TOP(X,Y) equipped with the Isbell topology may not be an S*-well-filtered space. Finally, we study the S*-well-filteredness of Smyth power spaces. In addition, Johnstone's non-sober dcpo example is shown to be S*-well-filtered yet it is not strongly well-filtered, thereby establishing an obvious distinction between these two classes of dcpos. |
| title | S*-well-filtered spaces and d*-spaces |
| topic | General Topology 06 Order, lattices, order algebraic structures, 54 General topology |
| url | https://arxiv.org/abs/2601.11281 |