Definition:Totally Pathwise Disconnected Space

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

• Equivalence of Definitions of Totally Pathwise Disconnected Space

• Definition:Totally Disconnected Space

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