# Coffee Mug and Doughnut are Homeomorphic

## Theorem

A doughnut and a mug coffee mug are homeomorphic.

## Proof

They are both solid objects with one hole.

A classical doughnut is in the shape of a torus.

That is, it is a solid figure with one hole.

The classic coffee-cup shape is a receptacle with a closed loop of china forming a handle.

The hole through which you put your fingers is homeomorphic to the hole in the doughnut.

$\blacksquare$