Every monotonically normal Čech-complete space is subcompact

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

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Every monotonically normal Čech-complete space is subcompact

Cited by 2 publications

References 6 publications

Mary Ellen Rudin and monotone normality

Mary Ellen Rudin and monotone normality

Domain representable Lindelöf spaces are cofinally Polish

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