How is possible that those shapes are equivalent in topology?

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.

(left pic is from post, right pic is super contrast enhanced to tease out line)

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


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.)


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

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General Topology

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