# Definition:Disconnected (Topology)/Set/Definition 2

## Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$ be a non-empty subset of $S$.

$H$ is a disconnected set of $T$ if and only if there exist open sets $U$ and $V$ of $T$ such that:

$H \subseteq U \cup V$
$H \cap U \cap V = \varnothing$
$U \cap H \ne \varnothing$

and:

$V \cap H \ne \varnothing$

## Also see

• Results about disconnected sets can be found here.