Tag Archives: path-connected spaces

Topology: Locally Connected and Locally Path-Connected Spaces

Locally Connected Spaces Recall that each topological space X is the set-theoretic disjoint union of its connected components, but in general (e.g. for X=Q) fails to be the topological disjoint union. The problem is that the connected components in general aren’t open … Continue reading

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Topology: Path-Connected Spaces

A related notion of connectedness is this: Definition. A path on a topological space X is a continuous map The path is said to connect x and y in X if f(0)=x and f(1)=y. X is said to be path-connected if any two points … Continue reading

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