Definition:Disconnected (Topology)

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This page is about disconnectedness in topology. For other uses, see Definition: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.