On the cardinality of power homogeneous Hausdorff spaces
Volume 192 / 2006
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.
