# Definition:Totally Separated Space

## Definition

### Definition 1

A topological space $T = \left({S, \tau}\right)$ is totally separated if and only if:

For every $x, y \in S: x \ne y$ there exists a separation $U \mid V$ of $T$ such that $x \in U, y \in V$.

### Definition 2

A topological space $T = \left({S, \tau}\right)$ is totally separated if and only if each of its quasicomponents is a singleton set.

## Also see

• Results about totally separated spaces can be found here.