Download PDF

locally connected∗
djao†
2013-03-21 14:06:29
A topological space X is locally connected at a point x ∈ X if every neighborhood U of x contains a connected neighborhood V of x. The space X is
locally connected if it is locally connected at every point x ∈ X.
A topological space X is locally path connected at a point x ∈ X if every
neighborhood U of x contains a path connected neighborhood V of x. The space
X is locally path connected if it is locally path connected at every point x ∈ X.
∗ hLocallyConnectedi created: h2013-03-21i by: hdjaoi version: h32912i Privacy setting:
h1i hDefinitioni h54D05i
† This text is available under the Creative Commons Attribution/Share-Alike License 3.0.
You can reuse this document or portions thereof only if you do so under terms that are
compatible with the CC-BY-SA license.
1