# Definition:Disconnected (Topology)

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

## Contents

## 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): Entry:**disconnected**