Category:Definitions/Hausdorff Spaces

This category contains definitions related to Hausdorff Spaces.
Related results can be found in Category:Hausdorff Spaces.

$\struct {S, \tau}$ is a Hausdorff space or $T_2$ space if and only if:

$\forall x, y \in S, x \ne y: \exists U, V \in \tau: x \in U, y \in V: U \cap V = \O$

That is:

for any two distinct elements $x, y \in S$ there exist disjoint open sets $U, V \in \tau$ containing $x$ and $y$ respectively.