Definition:Totally Disconnected Space

Definition
A topological space $T = \struct {S, \tau}$ 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 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

 * Totally Disconnected but Connected Set must be Singleton


 * Definition:Totally Pathwise Disconnected Space