Definition:Disconnected (Topology)

This page is about Disconnected in the context of topology. For other uses, see Disconnected.

Definition

Topological Space

A topological space $T$ is disconnected if and only if it is not connected.

Subset of Topological Space

$H$ is a disconnected set of $T$ if and only if it is not a connected set of $T$.

Points in Topological Space

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

Let $a, b \in S$.

Then $a$ and $b$ are disconnected (in $T$) if and only if they are not connected (in $T$).

Also see

• Results about disconnected spaces can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): disconnected