Definition:Disconnected (Topology)/Topological Space

Definition

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

Definition $1$

$T$ is disconnected if and only if $T$ is not connected.

Definition $2$

$T$ is disconnected if and only if there exist non-empty open sets $U, V \in \tau$ such that:

$S = U \cup V$

$U \cap V = \O$

That is, if there exists a partition of $S$ into open sets of $T$.

Also see

• Equivalence of Definitions of Disconnected Space

• Definition:Disconnected Set

• Results about disconnected spaces can be found here.