Countably compact inverse semigroups and Nyikos' problem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916943744729088 |
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| author | Bardyla, Serhii |
| author_facet | Bardyla, Serhii |
| contents | A regular separable first-countable countably compact space is called a Nyikos space. In this paper, we give a partial solution to an old problem of Nyikos by showing that each locally compact Nyikos inverse topological semigroup is compact. Also, we show that a topological semigroup $S$ that contains a dense inverse subsemigroup is a topological inverse semigroup, provided (i) $S$ is compact, or (ii) $S$ is countably compact and sequential. The latter result solves a problem of Banakh and Pastukhova and provides the automatic continuity of inversion in certain compact-like inverse semigroups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_13666 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Countably compact inverse semigroups and Nyikos' problem Bardyla, Serhii General Topology Group Theory A regular separable first-countable countably compact space is called a Nyikos space. In this paper, we give a partial solution to an old problem of Nyikos by showing that each locally compact Nyikos inverse topological semigroup is compact. Also, we show that a topological semigroup $S$ that contains a dense inverse subsemigroup is a topological inverse semigroup, provided (i) $S$ is compact, or (ii) $S$ is countably compact and sequential. The latter result solves a problem of Banakh and Pastukhova and provides the automatic continuity of inversion in certain compact-like inverse semigroups. |
| title | Countably compact inverse semigroups and Nyikos' problem |
| topic | General Topology Group Theory |
| url | https://arxiv.org/abs/2503.13666 |