# Definition:Totally Pathwise Disconnected Space

Jump to navigation
Jump to search

## Definition

### Definition 1

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

### Definition 2

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

## Also see

- Results about
**totally pathwise disconnected spaces**can be found here.