# Definition:Totally Disconnected Space

Jump to navigation Jump to search

## Definition

A topological space $T = \left({S, \tau}\right)$ is a totally disconnected space if and only if all components of $T$ are singletons.

That is, $T$ is a totally disconnected space if and only if it contains no non-degenerate connected sets.

## Also defined as

Because of Totally Disconnected but Connected Set must be Singleton, the definition for totally disconnected space is applied by some authors to a topological space containing at least $2$ elements.

## Also see

• Results about totally disconnected spaces can be found here.