Let X be a topological spaceMathworldPlanetmath. A (HausdorffPlanetmathPlanetmath) compactification of X is a pair (K,h) where K is a Hausdorff topological space and h:XK is a continuous functionMathworldPlanetmathPlanetmath such that

  • K is compactPlanetmathPlanetmath

  • h is a homeomorphism between X and h(X)

  • h(X)¯K=K where A¯K denotes closureMathworldPlanetmathPlanetmath in K for any subset A of K

h is often considered to be the inclusion mapMathworldPlanetmath, so that XK with X¯K=K.

Title compactification
Canonical name Compactification
Date of creation 2013-03-22 12:15:42
Last modified on 2013-03-22 12:15:42
Owner Evandar (27)
Last modified by Evandar (27)
Numerical id 8
Author Evandar (27)
Entry type Definition
Classification msc 54D35
Synonym Hausdorff compactification
Related topic Compact
Related topic AlexandrovOnePointCompactification