On Wallman bases and compactifications (Q2493342)

In this interesting paper, the author makes another stride in his long and deep study of Wallman bases. He gives necessary and sufficient conditions on a (not necessarily normal) Wallman basis of a \(T_1\)-space \(X\) for the induced compactification to be perfect, resp. one in which \(X\) is locally connected. He also characterizes those compactifications of a completely regular space \(X\), in which \(X\) is \(G_\delta\)-dense, by the existence of a certain kind of normal Wallman basis on \(X\).