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.
Arhangel'skii, A. and Tkachenko, M., Topological Groups and Related Structures, Atlantis Press, Amsterdam, 2008.
Arhangel'skii, A. and Tkachenko, M., Topological Groups and Related Structures, Atlantis Press, Amsterdam, 2008.)| false
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Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
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