nLab simply connected space

Definition

A simply connected topological space is a 1-connected topological space $X$: a connected space whose fundamental group is the trivial group:

$\pi_1(X) = \{\mathrm{e}\}$.

Equivalently: if it is a simply connected object of the (∞,1)-topos Top.

See n-connected object of an (infinity,1)-topos for more.

Related concepts

• connected topological space

• simple topological space

• nilpotent topological space