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.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Path-connected_space.svg/220px-Path-connected_space.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/9/95/Connected_and_disconnected_spaces.svg/220px-Connected_and_disconnected_spaces.svg.png)
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.
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