Noetherian $π$-bases and Telgársky's Conjecture
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909465793527808 |
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| author | Soyarslan, Servet Önal, Süleyman |
| author_facet | Soyarslan, Servet Önal, Süleyman |
| contents | We investigate Noetherian families and show that every topological space has a Noetherian $π$-base. We prove that if a topological space has some special Noetherian $π$-bases, then NONEMPTY has a 2-tactic in the Banach-Mazur game on a space $X$, denoted as $BM(X)$, whenever NONEMPTY has a winning strategy in BM(X). This result encompasses an important theorem of Galvin in this context and is related to Telgársky's conjecture on this subject. One of our examples is that any space $X$ with $πw(X)\leq ω_1$ has this special Noetherian $π$-base. We pose some questions about this topic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_05508 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Noetherian $π$-bases and Telgársky's Conjecture Soyarslan, Servet Önal, Süleyman General Topology We investigate Noetherian families and show that every topological space has a Noetherian $π$-base. We prove that if a topological space has some special Noetherian $π$-bases, then NONEMPTY has a 2-tactic in the Banach-Mazur game on a space $X$, denoted as $BM(X)$, whenever NONEMPTY has a winning strategy in BM(X). This result encompasses an important theorem of Galvin in this context and is related to Telgársky's conjecture on this subject. One of our examples is that any space $X$ with $πw(X)\leq ω_1$ has this special Noetherian $π$-base. We pose some questions about this topic. |
| title | Noetherian $π$-bases and Telgársky's Conjecture |
| topic | General Topology |
| url | https://arxiv.org/abs/2212.05508 |