Download semilocally simply connected

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts
no text concepts found
Transcript 
semilocally simply connected∗
djao†
2013-03-21 14:06:24
A topological space X is semilocally simply connected if, for every point
x ∈ X, there exists a neighborhood U of x such that the map of fundamental
groups
π1 (U, x) −→ π1 (X, x)
induced by the inclusion map U ,→ X is the trivial homomorphism.
A topological space X is connected, locally path connected, and semilocally
simply connected if and only if it has a universal cover.
∗ hSemilocallySimplyConnectedi created: h2013-03-21i by: hdjaoi version: h32911i Privacy setting: h1i hDefinitioni h54D05i h57M10i
† 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
Related documents