“For math to thrive, it has to connect to nature. There is no other way.” — Van Vu
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Point set topology models the idea of “closeness”, which is more metaphysical then physical(nature).
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I wouldn't say that point set topology has thrived, not as a self-contained area of research. It explored all kinds of pathological dead ends and ran out of steam. One semester is useful, but after that everyone moves on.
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yes! haha that's what i was trying to get at with awfully confusing meme .. my understanding is that point set topology didn't thrive for these very reasons you pointed out
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