Category:Hausdorff Spaces

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This category contains results about $T_2$ (Hausdorff) spaces.


$\left({S, \tau}\right)$ is a Hausdorff space or $T_2$ space if and only if:

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

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.

Subcategories

This category has the following 8 subcategories, out of 8 total.

Pages in category "Hausdorff Spaces"

The following 64 pages are in this category, out of 64 total.