This animation shows a classic example of homeomorphism: a coffee mug and a torus are topologically the same. Roughly speaking, a topological space is a geometric object and the homeomorphism is a continuous stretching and bending of the object into a new shape. The traditional joke is that topologists can't tell the coffee cup from which they are drinking from the donut they are eating, since a sufficiently pliable donut could be reshaped to the form of a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle.Image credit: Kieff