Source: wikibot/locally-connected-space
= Locally connected space
{wiki=Locally_connected_space}
In topology, a space is said to be **locally connected** at a point if every neighborhood of that point contains a connected neighborhood of that point. More formally, a topological space \\(X\\) is said to be **locally connected** if for every point \\(x \\in X\\) and every neighborhood \\(U\\) of \\(x\\), there exists a connected neighborhood \\(V\\) of \\(x\\) such that \\(V \\subseteq U\\).