Difference between revisions of "Hausdorff space"
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| − | 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''' (or '''T<sub>2</sub> spaces''') 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. |
| − | + | The subspace of a Hausdorff space is a Hausdorff space; the product of 2 Hausdorff spaces is a Hausdorff space. | |
| − | [[Category: | + | |
| + | The most important property of Hausdorff spaces is that sequences, nets and filters converge to a unique point. | ||
| + | [[Category:Topology]] | ||
Latest revision as of 13:50, July 13, 2016
Hausdorff space (or T2 spaces) 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.
The subspace of a Hausdorff space is a Hausdorff space; the product of 2 Hausdorff spaces is a Hausdorff space.
The most important property of Hausdorff spaces is that sequences, nets and filters converge to a unique point.