Abhijeet Mulgund's Personal Webpage

Search

Search IconIcon to open search

Path-Connected Component

Last updated Nov 1, 2022

# Definition

Let $X$ be a Topological Space. Then $P \subset X$ is a Path-Connected Component of $X$ if $P$ is a Maximal (wrt Subset Relation) path-connected set. That is, if $P’ \subset X$ is Path-Connected and $P \subset P’$, then $P = P’$.