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Let $M$ be a topological manifold.
$M$ is called a connected manifold if and only if $M$ is a connected topological space.
$M$ is called a (path-) connected manifold if and only if $M$ is a path-connected topological space.
- 2011: John M. Lee: Introduction to Topological Manifolds (2nd ed.): $\S 4$: Connectedness and Compactness. Connectedness. Definitions and Basic Properties