Extensions of topological spaces with strongly-discrete remainder (Q1295176)

Alexandroff's one-point compactification is one of the most well-known constructions in all topology. In this paper the construction of the Alexandroff one-point compactification is extended to prove paracompact extensions of locally compact Hausdorff spaces with strongly-discrete remainder. The main theorem is that if \(X\) is a locally compact Hausdorff space, then the remainder \(X^*\smallsetminus X\) is locally compact Hausdorff and paracompact, and hence is a disjoint sum of \(\sigma\)-compact spaces.