# Definition:Totally Pathwise Disconnected Space

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## Definition

### Definition 1

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

### Definition 2

A topological space $T = \left({S, \tau}\right)$ is **totally pathwise disconnected** if and only if the only continuous mappings from the closed unit interval $\left[{0 \,.\,.\, 1}\right]$ to $T$ are constant mappings.

## Also see

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