Category:Definitions/T5 Spaces

This category contains definitions related to $T_5$ spaces in the context of topology.
Related results can be found in Category:T5 Spaces.

$\struct {S, \tau}$ is a $T_5$ space if and only if:

$\forall A, B \subseteq S, A^- \cap B = A \cap B^- = \O: \exists U, V \in \tau: A \subseteq U, B \subseteq V, U \cap V = \O$

That is:

$\struct {S, \tau}$ is a $T_5$ space when for any two separated sets $A, B \subseteq S$ there exist disjoint open sets $U, V \in \tau$ containing $A$ and $B$ respectively.