semilocally simply connected

A topological spaceMathworldPlanetmath X is semilocally simply connected if, for every point xX, there exists a neighborhood U of x such that the map of fundamental groupsMathworldPlanetmathPlanetmath


induced by the inclusion mapMathworldPlanetmath UX is the trivial homomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath.

A topological space X is connected, locally path connected, and semilocally simply connected if and only if it has a universal coverMathworldPlanetmath.

Title semilocally simply connected
Canonical name SemilocallySimplyConnected
Date of creation 2013-03-22 12:38:46
Last modified on 2013-03-22 12:38:46
Owner djao (24)
Last modified by djao (24)
Numerical id 6
Author djao (24)
Entry type Definition
Classification msc 54D05
Classification msc 57M10
Synonym semilocally 1-connected
Synonym locally relatively simply connected
Related topic Connected2
Related topic SimplyConnected
Related topic ConnectedSpace
Related topic LocallyConnected