Definition:Totally Pathwise Disconnected Space/Definition 2

Definition

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

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

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness: Disconnectedness