fun stackexchange answer i just wrote meditating on the surprisingly deep question of what it means for a shape to have an "inside" or an "outside"
math.stackexchange.com/a/3849614/232
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That's really elegant, QC. Thank you.
I notice my gut looks at the hyperboloid example and says "That's not tricky! It has two interiors and one exterior." I think it's using convexity as a fallback when there's no bound.
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ha. i suppose the two interiors are capable of holding water if gravity is oriented appropriately...
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huh this triggered a thought about another possible definition of "inside" specific to subspaces of R^n. (we can say a point x is inside a region R if every ray emitted from x eventually hits R.) will edit the answer with some further thoughts about this...
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more stuff!
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had some more thoughts about "insideness"
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