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Maximal densely countably compact topologies

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Abstract

A topological space X is densely countably compact if it possesses a dense subspace D with the property that every infinite subset of D has an accumulation point in X. We study topologies which are maximal with respect to this property; in particular we show that a T 1 densely countably compact space is maximal densely countably compact if and only if it is a scattered Fréchet SC-space of scattering order 2.

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Authors and Affiliations

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

    J. A. Martínez-Cadena & R. G. Wilson

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  1. J. A. Martínez-Cadena
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  2. R. G. Wilson
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Correspondence to R. G. Wilson.

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Research supported by CONACyT grant CB-2012-01-178103 (Mexico).

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Martínez-Cadena, J.A., Wilson, R.G. Maximal densely countably compact topologies. Acta Math. Hungar. 151, 259–270 (2017). https://doi.org/10.1007/s10474-016-0684-0

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  • DOI: https://doi.org/10.1007/s10474-016-0684-0

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