Topology and geometry, for example, have their 'differential counterparts' (as well as 'algebraic'). What is required of a mathematical discipline for there to exist such a subfield? For example, why isn't 'differential knot theory' a thing?
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For the last: Because knots are inherently discrete – Hagen von Eitzen Mar 24 '15 at 19:53
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So a 'prerequisite', if you will, is that the structures be continuous and/or non-discrete? – galois Mar 24 '15 at 19:59
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@HagenvonEitzen: does this preclude knot theory from being the subject of the "calculus of finite differences"? – abiessu Mar 24 '15 at 20:04