Difference between revisions of "Locally compact"
Jump to navigation
Jump to search
m (Reverted edits by K (Talk); changed back to last version by DrSandstone) |
m |
||
| Line 1: | Line 1: | ||
| − | |||
| − | |||
A [[topological space]] X is '''locally compact''' if every point in X has a neighbourhood that is contained in a compact subspace of X. | A [[topological space]] X is '''locally compact''' if every point in X has a neighbourhood that is contained in a compact subspace of X. | ||
'''Important Theorem''': Every locally compact [[Hausdorff space]] has a [[one-point compactification]]. | '''Important Theorem''': Every locally compact [[Hausdorff space]] has a [[one-point compactification]]. | ||
[[category: Topology]] | [[category: Topology]] | ||
Revision as of 22:06, December 14, 2009
A topological space X is locally compact if every point in X has a neighbourhood that is contained in a compact subspace of X.
Important Theorem: Every locally compact Hausdorff space has a one-point compactification.