Definition:Path Component/Maximal Path-Connected Set
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Definition
Let $T$ be a topological space.
The path component of $T$ containing $x$ is defined as:
- the maximal path-connected set of $T$ that contains $x$.
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