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. | The subspace of a Hausdorff space is a Hausdorff space; the product of 2 Hausdorff spaces is a Hausdorff space. | ||
Revision as of 02:13, April 7, 2007
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.