Topological Manifold is Locally Connected

This article needs proofreading. Please check it for mathematical errors. If you believe there are none, please remove {{Proofread}} from the code. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Proofread}} from the code.

Theorem

Let $M$ be a topological manifold.

Then $M$ is a locally connected space.

Proof

By definition of manifold:

$M$ is a locally Euclidean space

The result follows from Locally Euclidean Space is Locally Connected

$\blacksquare$