Coffee Mug and Doughnut are Homeomorphic
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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.
$\blacksquare$
Also see
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: $3.6$: Homeomorphisms: Examples $3.6.2 \ \text{(e)}$