Difference between revisions of "One-point compactification"
Jump to navigation
Jump to search
m |
|||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | If Y is a compact, [[Hausdorff space]]; X is a topological space such that Y-X contains one element and the closure of X equals Y; then Y is the one-point compactification of X. | + | If Y is a compact, [[Hausdorff space]]; X is a topological space such that Y-X contains one element and the closure of X equals Y; then Y is the one-point compactification of X. The One-point compactification is the minimal compactification one can perform on X. A space X has a one-point compactification if and only if it is itself locally compact and Hausdorff. |
| − | [[ | + | [[Category:Topology]] |
Latest revision as of 14:56, January 18, 2009
If Y is a compact, Hausdorff space; X is a topological space such that Y-X contains one element and the closure of X equals Y; then Y is the one-point compactification of X. The One-point compactification is the minimal compactification one can perform on X. A space X has a one-point compactification if and only if it is itself locally compact and Hausdorff.