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

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–Čech compactification of X if X is Tychonoff.