Abstract
We study three subclasses of the class of pseudocompact spaces. We answer two open questions concerning cellular-compact spaces and another concerning cellular-Lindelöf spaces and introduce and study three other subclasses of the class of feebly compact spaces, namely the class of cellular-countably-compact spaces, that of the cellular-sequentially-compact spaces and that of the cellular-compact-metrizable spaces. We show that it is independent of ZFC whether or not a cellular-compact-metrizable LOTS is metrizable.
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We thank the referees for many suggestions which have improved the paper.
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Ofelia T. Alas, Lucia R. Junqueira and Marcelo D. Passos were supported by FAPESB, Grant APP0072/2016.
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Alas, O.T., Junqueira, L.R., Passos, M.D. et al. On cellular-compactness and related properties. RACSAM 114, 101 (2020). https://doi.org/10.1007/s13398-020-00833-3
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DOI: https://doi.org/10.1007/s13398-020-00833-3
Keywords
- Cellular-compact space
- Cellular-countably-compact space
- Cellular-sequentially-compact space
- Cellular-compact-metrizable space
- Pseudocompact space
- Feebly compact space
- Weakly Lindelöf space
- Souslin line
- Lusin space