Connected manifold

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

This article defines a property of manifolds and hence also of topological spaces

Definition

A connected manifold is a connected space which is also a manifold.

Note that since any manifold is locally path-connected, a connected manifold is also path-connected.

Relation with other properties

Stronger properties

• Compact connected manifold

Weaker properties

• Homogeneous space: For full proof, refer: Connected manifold implies homogeneous