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So what you are saying is, if I dig a hole that doesn't go anywhere, then that's not really a hole?
Topologically, yes. Coincidentally, "Hole to Nowhere" is the best Talking Heads parody album.
Heh I will have to check that out!
In topology, yes. It must go through to count.
That's fascinating. So most of what I would call "holes" are what, in topographical terms, hollows? Depressions?
I don't even know if they have a name for that since it can simply be undone by stretching the object, which is allowed under topological rules.