User:Anghel/Sandbox

Definition
Let $T = \struct{S, \tau}$ be a path-connected topological space.

$T$ is simply connected if the fundamental group $\map {\pi_1}{ T }$ is trivial.

$T$ is simply connected if all loops in $T$ with identical base points are path-homotopic.

$T$ is simply connected if all paths in $T$ are freely homotopic.

$T$ is simply connected if all loops in $T$ are nulhomotopic.

Links

 * Fundamental Group is Independent of Base Point for Path-Connected Space
 * Homotopy Characterisation of Simply Connected Sets

Category:Definitions/Simply Connected Spaces]] Category:Definitions/Topology]] Category:Definitions/Algebraic Topology]]