Definition:Totally Separated Space/Definition 1

Definition
A topological space $T = \left({S, \tau}\right)$ is totally separated :
 * For every $x, y \in S: x \ne y$ there exists a separation $U \mid V$ of $T$ such that $x \in U, y \in V$.

Also see

 * Equivalence of Definitions of Totally Separated Space