Round 8: Tossup 19

If both a bijection between topological spaces and its inverse have this property, it is called a homeomorphism. If a function (10[1])scales the distance between two points by at most a constant, it has a form of this property named for Rudolf Lipschitz. A function has this property if and only if the pre-image of any open set is itself open. On an interval [a, b] (“a b”), a function f with this property will take all values between (10[1])[read slowly] f (10[1])of a and f of b (10[1])by (10[1])the intermediate value theorem. (10[1])A function has this property if it equals its limit at every point. For (10[1])10 points, name this property of a function that can be defined informally as being able to draw its graph without taking the pen off the paper. ■END■

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