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Mathematically It's one. Think of a disk, like a CD, does it have one hole or two? One, right? Now imagine you can make it thicker, I.e. increase the height, and then reduce the outer radius... Making it progressively more straw-like. At what point does it stop having 1 hole and begin to have 2?
Topologically they're the same shape.
I'm sure Matt Parker has a video on this topic in YouTube. Here
The specific field is topology fyi
If I dig a hole, how many holes is it?
Zero unless you reach Australia
Holes in the hole? 0
Holes in the top layer of the ground? 1