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'''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.
'''Hausdorff space''' (or '''T<sub>2</sub> spaces''') is a [[topological space]] in which, for any pair of indistinct points x and y, there exist disjoint closed sets U and V, such that x is in U and x 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.
The most important property of Hausdorff spaces is that sequences, nets and filters converge to a unique point.
The most important property of Hausdorff spaces is that sequences, nets and filters converge to a unique point.
An Etale space provides an example of a space that is not T<sub>2</sub>.
[[category: Topology]]
[[category: Topology]]