Definition:Connected Manifold

Definition

Let $M$ be a topological manifold.

Definition 1

$M$ is called a connected manifold if and only if $M$ is a connected topological space.

Definition 2

$M$ is called a (path-) connected manifold if and only if $M$ is a path-connected topological space.

Also see

• Equivalence of Definitions of Connected Manifold

Sources

• 2011: John M. Lee: Introduction to Topological Manifolds (2nd ed.): $\S 4$: Connectedness and Compactness. Connectedness. Definitions and Basic Properties