compactification
Let be a topological space. A (Hausdorff) compactification of is a pair where is a Hausdorff topological space and is a continuous function such that
-
•
is compact
-
•
is a homeomorphism between and
-
•
where denotes closure in for any subset of
is often considered to be the inclusion map, so that with .
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 |