Category:T4 Spaces

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This category contains results about $T_4$ spaces in the context of Topology.


$T = \left({S, \tau}\right)$ is a $T_4$ space if and only if:

$\forall A, B \in \complement \left({\tau}\right), A \cap B = \varnothing: \exists U, V \in \tau: A \subseteq U, B \subseteq V, U \cap V = \varnothing$

That is, for any two disjoint closed sets $A, B \subseteq S$ there exist disjoint open sets $U, V \in \tau$ containing $A$ and $B$ respectively.

Subcategories

This category has the following 5 subcategories, out of 5 total.

E

F

N

P