Category:Definitions/Simply Connected Spaces
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This category contains definitions related to Simply Connected Spaces.
Related results can be found in Category: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.
Pages in category "Definitions/Simply Connected Spaces"
The following 6 pages are in this category, out of 6 total.