Transfer of information about \(\beta\) N - N via open remainder maps
The purpose of the paper is to give new tools, in which the information is passed indirectly from \(\beta\) N-N to the Čech-Stone remainder of other spaces. Among them there is the following Open Mapping Lemma: if X is realcompact and non-compact and \(x\in \beta X-X\), then there exists a compact subset of \(\beta\) X-X which contains x and admits an open mapping onto \(\beta\) N-N. Using these theorems, as well as some similar but much more complicated, the author obtained significant new results concerning P-points, \({\mathfrak c}\)-points, \(G_{\delta}\)-subsets, Baire number, character and Hausdorff gaps in the Čech-Stone remainders of locally compact realcompact spaces. The same problems are also investigated in the classes of \(\sigma\)-compact and non-pseudocompact spaces.
Cech-Stone remainder of the countable discrete space
Čech-Stone remainders of locally compact realcompact spaces
\(\sigma \) -compact and non- pseudocompact spaces
scientific article; zbMATH DE number 4166041