Alexandrov one-point compactification

The Alexandrov one-point compactification of a non-compact topological spaceMathworldPlanetmath X is obtained by adjoining a new point and defining the topology on X{} to consist of the open sets of X together with the sets of the form U{}, where U is an open subset of X with compactPlanetmathPlanetmath complement.

With this topology, X{} is always compact. Furthermore, it is HausdorffPlanetmathPlanetmath if and only if X is Hausdorff and locally compact.

Title Alexandrov one-point compactification
Canonical name AlexandrovOnepointCompactification
Date of creation 2013-03-22 13:47:54
Last modified on 2013-03-22 13:47:54
Owner yark (2760)
Last modified by yark (2760)
Numerical id 9
Author yark (2760)
Entry type Definition
Classification msc 54D35
Synonym one-point compactification
Synonym Alexandroff one-point compactification
Synonym Aleksandrov one-point compactification
Synonym Alexandrov compactification
Synonym Aleksandrov compactification
Synonym Alexandroff compactification
Related topic Compactification