The Alexandroff extension is a concept in topology, specifically in the study of topological spaces. It can be seen as a method to extend a given topological space by adding a "point at infinity," thereby creating a new space that retains certain properties of the original.
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The one-point compactification of a locally compact noncompact Hausdorff space adjoins one point whose neighbourhoods are complements of compact subsets. The result is compact Hausdorff.