Stone-Čech remainders of nowhere locally compact spaces
All topological spaces are completely regular and Hausdorff, and we suppose that \(X\) is a nowhere locally compact space. The authors show that, for every compactification \(\alpha X\) of \(X\) such that the space \(\alpha X-X\) is extremally disconnected, we have \(\alpha X=\beta X\), where \(\beta X\) is the Čech-Stone compactification of \(X\). Furthermore, equivalent conditions are given for the space \(\beta X-X\) to be extremally disconnected. These results extend those of \textit{E. K. van Douwen} [Topology Appl. 47, No.~3, 165--171 (1992; Zbl 0766.54024)]. In conclusion, a characterization of the property \(\beta X-X\) being 0-dimensional by means of free \(z\)-ultrafilters in \(X\) is presented.
scientific article; zbMATH DE number 5651927