nLab
simply connected space

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

${\pi }_1(X)=\{e\}$.

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

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