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Topological Manifolds Connected iff Path-Connected

Last updated Nov 1, 2022

# Statement

Let $M$ be a Topological Manifold of Manifold Dimension $n$. $M$ is Connected If and Only If it is Path-Connected.

# Proof

Topological Manifolds are Locally Path-Connected and Locally Path-Connected Spaces are Path-Connected iff they are Connected. $\blacksquare$