Simply connected space

topological space which has no holes through it

A space (or shape) is called simply connected if it is all one piece and does not have any "holes" that pass all the way through it. For example, a ball is simply connected, but a doughnut is not.

A path between two points in a simply connected space.
The green shape ('A') is simply connected. The blue shape ('B') is not simply connected.

More formally, being "one piece" means a shape is path-connected, which means there is a path from any point inside the shape to any other which does not leave the shape.