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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
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