Abhijeet Mulgund's Personal Webpage

Search

Search IconIcon to open search

Path-Connected Components of Topological Manifolds are Open

Last updated Nov 1, 2022

# Statement

Let $X$ be a Topological Manifold of Manifold Dimension $n$. Then every Path-Connected Component $C \subset X$ is Open.

# Proof

Topological Manifolds are Locally Path-Connected and Path-Connected Components of Locally Path-Connected Spaces are Open. $\blacksquare$