The Alexandroff extension Let be a topological space. Put and topologize by taking as open sets all the open sets in X together with all sets of the form where C is closed and compact in X. Here, denotes the complement of in Note that is an open neighborhood of and thus any open cover of will contain all except a compact subset of implying that is compact .
The Alexandroff extension Let be a topological space. Put and topologize by taking as open sets all the open sets in X together with all sets of the form where C is closed and compact in X. Here denotes the complement of in Note that is an open neighborhood of and thus any open cover of will contain all except a compact subset of implying that is compact .