Category:Simply Connected Spaces

This category contains results about Simply Connected Spaces.
Definitions specific to this category can be found in Definitions/Simply Connected Spaces.

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

Definition by fundamental group

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

Definition by path-homotopy of loops

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

Definition by path-homotopy of paths

$T$ is said to be simply connected if all paths in $T$ with identical initial points and final points are path-homotopic.

Definition by null-homotopy

$T$ is said to be simply connected if all loops in $T$ are path-homotopic with a constant loop.