Game strategies yield remote points
Let X be a nonpseudocompact space. A point \(p\in \beta X-X\) is said to be a remote point of X if for every nowhere dense subset D of X, \(p\not\in Cl_{\beta X}D\). \textit{S. B. Chae} and \textit{J. H. Smith} [Top. Appl. 11, 243-246 (1980; Zbl 0434.54016)] and independently \textit{E. K. van Douwen} [Remote points, Diss. Math. 188 (1981; Zbl 0525.54018)] proved the existence of a large class of spaces having remote points. In this interesting paper the authors prove among other things that a product of metrizable spaces has remote points if and only if it is not compact. Interestingly, their technique of proof uses games.
\(\sigma \)-locally finite \(\pi \)-base
scientific article; zbMATH DE number 4042813
scientific article