A net and open-filter process of compactification and the Stone-Cech, Wallman compactifications

摘要

By a characterization of compact spaces in Section 1, a process of obtaining a compactification (X~*, k) of an arbitrary topological space X is described in Section 2 by a combined approach of nets and open filters. The Wallman compactification can be embedded in X~* if X is Hausdorff and by a little modification, the compactification (X_β~*, k) of X is the Stone-Cech compactification of X if X is Tychonoff.