How is possible that those shapes are equivalent in topology?

Question

I recently started to study topology, I have no idea about the subject so my question could be very simple but I need a clear explanation. It is about the page number 19 of Introducton to Topology by Colin Adams and Robert Franzosa; it said that the shapes:

are equivalent in topology, but one has just one hole and the other has two. is possible to add holes or stick holes?

Answer 1

Look a bit more closely at the second picture. There's a couple of little dotted lines connecting the two holes that may be a bit hard to see.

That is meant to convey the impression they are the two ends of a single, long, curved hole through the interior.

Answer 2

The "two holes" in that sphere are two ends of the same hole. (That is, if you drilled one hole all the way through a sphere, you would end up with something that looked very much like your picture.)

Answer 3

You may also notice the tunel, which I agree with you it is not clear in this photo.

Answer 4

The cuboid and the sphere are topological euvivalent. Drill a hole through each body as indicated by the arrow. The resulting bodies are still topological equivalent.