Difference between revisions of "Locally compact"
Jump to navigation
Jump to search
m |
DavidB4-bot (talk | contribs) (→top: clean up & uniformity) |
||
| (6 intermediate revisions by 6 users not shown) | |||
| 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]] |
Latest revision as of 15:28, July 13, 2016
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.