Answer to Question #6941 in Differential Geometry | Topology for Akhtar Rasool

Question

Dear Expert how will we show that a coffee cup is homeomorphic to doughnut .f any approach please explain.

Answer 1

A continuous deformation between a coffee mug and a donut illustrating that they are homeomorphic.
Continuous deformation is shown here
The surfaces of a donut and a coffee cup (with one handle) are considered equivalent because both have a single hole.