Two Moore spaces on which every continuous real-valued function is constant (Q1202800)

A point \(p\) of a connected topological space \(X\) is called a dispersion point if the space \(X\backslash\{p\}\) is totally disconnected. Strengthening earlier results of different authors it is shown that there exists a separable Moore space \(X\) with a dispersion point such that every real-valued continuous function on \(X\) is constant. There also exists a screenable (hence metacompact) Moore space with a dispersion point on which every real-valued continuous function is constant.