Definition:Locally Path-Connected Space/Definition 3
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Definition
A topological space $T = \struct {S, \tau}$ is a locally path-connected space if and only if it has a basis consisting of path-connected sets in $T$.
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
- 2003: John M. Lee: Introduction to Smooth Manifolds: $\S 1.1$: Smooth Manifolds. Topological Manifolds