Definition:Totally Disconnected Space

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

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

Also defined as
Because of Trivial Topological Space is Connected and Totally Disconnected, the definition for totally disconnected space is applied by some authors to a topological space containing at least $2$ elements.

Also see

 * Trivial Topological Space is Connected and Totally Disconnected


 * Definition:Totally Pathwise Disconnected Space