On the cardinality of power homogeneous Hausdorff spaces

Volume 192 / 2006

G. J. Ridderbos Fundamenta Mathematicae 192 (2006), 255-266 MSC: 54A25, 54B10. DOI: 10.4064/fm192-3-5

Abstract

We prove that the cardinality of power homogeneous Hausdorff spaces $X$ is bounded by $d(X)^{\pi \chi (X)}$. This inequality improves many known results and it also solves a question by J. van Mill. We further introduce $\Delta $-power homogeneity, which leads to a new proof of van Douwen's theorem.

Authors

  • G. J. RidderbosFaculty of Sciences, Division of Mathematics
    Vrije Universiteit
    De Boelelaan 1081A
    1081 HV Amsterdam, The Netherlands
    e-mail

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