A strengthening of the Čech-Pospišil theorem
For a space \(X\), dis\((X)\) denotes the smallest infinite cardinal \(\kappa\) such that \(X\) can be covered by \(\kappa\) discrete subspaces. A result is shown whose corollary is the following improvement of the famous Čech-Pospišil theorem [\textit{E. Čech} amd \textit{B. Pospišil}, Publ. Fac. Sci. Univ. Masaryk 258, 1--14 (1938; Zbl 0019.08903)]: if \(X\) is a compact Hausdorff space with \(\chi(x,X) \geq \kappa\) for each \(x\in X\), then dis\((X) \geq 2^{\kappa}\).
scientific article; zbMATH DE number 5365225