Definition:Locally Connected Space/Definition 1

Definition

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

Also see

• Equivalence of Definitions of Locally Connected Space

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $6.5$: Components: Definition $6.5.5$