Definition:Locally Connected Space/Definition 3

Definition

A topological space $T = \struct{S, \tau}$ is locally connected if and only if it has a basis consisting of connected sets in $T$.

Also see

• Equivalence of Definitions of Locally Connected Space

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