one-point compactification

one-point compactification

[′wən ‚pȯint kəm‚pak·tə·fə′kā·shən] (mathematics) The one-point compactification X̄ of a topological space X is the union of X with a set consisting of a single element, with the topology of X̄ consisting of the open subsets of X and all subsets of X̄ whose complements in X̄ are closed compact subsets in X. Also known as Alexandroff compactification.