Definition:T5 Space/Definition 1

Definition
Let $T = \struct {S, \tau}$ be a topological space.

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


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

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.

Also see

 * Equivalence of Definitions of $T_5$ Space