Equivalent Definition for Locally Path-Connected
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Theorem
Let $T = \left({X, \vartheta}\right)$ be a topological space.
Then $T$ is locally path-connected iff the path components of open subsets of $X$ are also open in $X$.
Proof
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Sources
- Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 4$
