领域可表示Lindelöf空间是cofinally Polish

Pub Date : 2019-12-01 DOI:10.1556/012.2019.56.4.1442

V. Tkachuk

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引用次数: 2

摘要

证明了对于任意cofinally Polish spaceX, x的非空开子集的每一个局部有限族都是可数的。在σ-紧空间中，Lindelöf域可表征空间是协精的，域可表征性与次紧性是一致的。结果表明，对于空间为Lindelöf Σ-property的拓扑群g，当且仅当空间为Čech-complete时，空间域才可表示。我们的研究结果解决了几个公开发表的开放性问题。

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Domain representable Lindelöf spaces are cofinally Polish

We prove that, for any cofinally Polish spaceX, every locally finite family of non-empty open subsets ofXis countable. It is also established that Lindelöf domain representable spaces are cofinally Polish and domain representability coincides with subcompactness in the class ofσ-compact spaces. It turns out that, for a topological groupGwhose space has the Lindelöf Σ-property, the spaceGis domain representable if and only if it is Čech-complete. Our results solve several published open questions.

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