Hausdorff space (or T2 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 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 T2.