Difference between revisions of "Hausdorff space"
Jump to navigation
Jump to search
m |
|||
| Line 1: | Line 1: | ||
Hausdorff space is a [[topological space]] in which, for any pair of distinct points x and y, there exist disjoint open sets U and V, such that x is in U and y is in V. Almost all spaces studied in analysis are Hausdorff. | Hausdorff space is a [[topological space]] in which, for any pair of distinct points x and y, there exist disjoint open sets U and V, such that x is in U and y is in V. Almost all spaces studied in analysis are Hausdorff. | ||
| − | An important property of Hausdorff spaces is that sequences and | + | An important property of Hausdorff spaces is that sequences, nets and filters converge to a unique point. |
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 03:48, March 21, 2007
Hausdorff space is a topological space in which, for any pair of distinct points x and y, there exist disjoint open sets U and V, such that x is in U and y is in V. Almost all spaces studied in analysis are Hausdorff.
An important property of Hausdorff spaces is that sequences, nets and filters converge to a unique point.