Simply connected space

A simply connected space is path connected and has trivial fundamental group: every closed loop contracts to a point. The three-sphere is simply connected, whereas Real projective space ${\mathbb{RP}}^3$ has fundamental group ${\mathbb{Z}}_2$.

In topology, a space is said to be **simply connected** if it is both path-connected and any loop (closed path) in the space can be continuously contracted to a point.