Abstract
We introduce the notion of a cellular-compact space and prove that cellular compactness is a nice property that implies cellular Lindelöfness. The class of cellular-compact spaces is preserved by continuous images and finite unions, as well as by regular closed subsets and extensions. It is established that cellular-compact spaces must be pseudocompact but not necessarily countably compact. We prove that first countable cellular-compact regular spaces are countably compact and their cardinality does not exceed \({2^{\omega}}\). We also show that a collectionwise normal Fréchet–Urysohn cellular-compact space need not be compact and there exist Fréchet–Urysohn cellular-compact spaces that do not have a dense countably compact subspace.
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Tkachuk, V.V., Wilson, R.G. Cellular-compact spaces and their applications. Acta Math. Hungar. 159, 674–688 (2019). https://doi.org/10.1007/s10474-019-00968-9
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DOI: https://doi.org/10.1007/s10474-019-00968-9
Key words and phrases
- cellular-compact space
- cellular-Lindelöf space
- weakly Lindelöf space
- disjoint local \(\pi\)-base
- first countable space
- maximal cellular-compact space