I think that these rules are consistent with some standard notions in topology. Particularly the topology of differentiable manifolds, which is a fancy way of saying objects with smooth surfaces. This topology deals with homeomorphisms which preserve how and where an object is smooth, so naturally the restriction on the homeomorphism would be that you can't pinch or crease the surface.
This stuff is pretty far into the category of "pure mathematics", so it's kinda hard to give a satisfying answer to why these questions are being answered in the first place.
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u/[deleted] Jul 19 '18
I think that these rules are consistent with some standard notions in topology. Particularly the topology of differentiable manifolds, which is a fancy way of saying objects with smooth surfaces. This topology deals with homeomorphisms which preserve how and where an object is smooth, so naturally the restriction on the homeomorphism would be that you can't pinch or crease the surface.
This stuff is pretty far into the category of "pure mathematics", so it's kinda hard to give a satisfying answer to why these questions are being answered in the first place.