| Popis: |
A topological space X is called resolvable at a point \(x_0\) if \(X\setminus \{x_0\}\) contains two disjoint subsets A, B such that \(x_0\in \overline{A}, x_0\in \overline{B}\). In this paper we prove that if a regular topological space X is irresolvable at some non-isolated point \(x_0 \in X\), then X contains an infinite discrete in X family \(\mathfrak {{W}}=\{W_\alpha \}\) of non-empty open subsets of X. Therefore, every feebly compact regular space is resolvable at any non-isolated point. Consequently, every pseudocompact space is resolvable at any non-isolated point. |
