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

  • Results about totally pathwise disconnected spaces can be found here.