Answer
The given statement is true.
Work Step by Step
Topology is a modern branch of geometry in which shapes, unlike Euclidean geometry, are not rigid. In topology, shapes can be twisted, bent or stretched to form another shape. The objects are classified by the genus, which is the number of holes in the object. Objects having the same genus are referred to be topologically equivalent.
The number of cuts that can be made in that object without rendering that object into two pieces is known as its genus. As a doughnut and compact disc both have the same number of holes, that is, one and only one complete cut can be made without cutting these objects into two pieces, therefore these two objects are topologically equivalent.
Hence, the given statement is true.
