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.
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.