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When is a cellular-countably-compact space, countably compact?

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We continue the study of cellular-compact spaces and the larger class of cellular-countably-compact spaces. We give a number of sufficient conditions involving local bases and local \(\pi \)-bases in order that a cellular-countably-compact space be countably compact and some conditions which imply that a topology is maximal with respect to being cellular-countably-compact are obtained. We also consider the compact productivity of the previously mentioned properties and give a characterization of those spaces whose product with a compact space is almost cellular-countably-compact.

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Acknowledgements

We wish to thank the referees for their detailed comments, for correcting a number of small errors in the original version of this paper and for bringing to our attention a number of recent articles on topics related to the subject under study here.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo, 05314-970, Brasil

    Ofelia T. Alas

  2. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Avenida San Rafael Atlixco, #186, Apartado Postal 55-532, Mexico City, 09340, D.F., Mexico

    L. Enrique Gutiérrez-Domínguez & Richard G. Wilson

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  1. Ofelia T. Alas
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  2. L. Enrique Gutiérrez-Domínguez
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  3. Richard G. Wilson
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Correspondence to Richard G. Wilson.

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Alas, O.T., Gutiérrez-Domínguez, L.E. & Wilson, R.G. When is a cellular-countably-compact space, countably compact?. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 163 (2023). https://doi.org/10.1007/s13398-023-01495-7

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