Simply connected space

Symbol-free definition
A topological space is said to be simply connected if it satisfies the following equivalent conditions:


 * It is path-connected, and any loop at any point is homotopic to the constant loop at that point
 * It is path-connected, and its fundamental group is trivial

Metaproperties
An arbitrary product of simply connected spaces is simply connected. This follows from the fact that the fundamental group of a product of path-connected spaces, is the product of their fundamental groups.

A retract of a simply connected space is simply connected. This follows from the fact that the fundamental group of a retract is a group-theoretic retract of the fundamental group of the whole space.