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H-closed; cardinal functions; measurable cardinals
The cardinal functions of pseudocharacter, closed pseudocharacter, and character are used to examine H-closed spaces and to contrast the differences between H-closed and minimal Hausdorff spaces. An H-closed space $X$ is produced with the properties that $|X|>2^{2^{\psi (X)}}$ and $\overline{\psi}(X)>2^{\psi(X)}$.
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[E] Engelking R.: General Topology. Warsaw, 1977. MR 0500780 | Zbl 0684.54001
[H] Hodel R.G.: Cardinal function I. in Handbook of Set-theoretical Topology, K. Kunen and J. Vaughan ed., North Holland-Amsterdam, 1984. MR 0776619
[PW] Porter J.R., Woods R.G.: Extensions and Absolutes of Hausdorff Spaces. Springer-Verlag, Berlin, 1988. MR 0918341 | Zbl 0652.54016
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