Round 6: Tossup 19

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

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