If both a bijection between topological spaces and its inverse (-5[1])have this property, (10[1])it is called (10[1])a homeomorphism. (10[7]-5[3])If a (10[1])function (10[2])scales the distance between two (10[1])points by at most a constant, (-5[1])it has a form of this property (10[2])named for Rudolf Lipschitz. (10[12]-5[1])A (10[1])function (10[3])has (10[1])this (10[3])property (10[3])if and only (10[1])if (10[1])the pre-image of any open set (-5[1])is itself open. (10[2])On an interval (10[1]-5[1])[a, b] (“a b”), a function f with this property will take (10[1])all values (10[1])between (10[6])[read (10[5])slowly] (10[3])f (10[5]-5[1])of (10[1])a (10[1])and (10[4])f (10[12]-5[2])of (10[2])b (10[3])by (10[3])the intermediate (10[9]-5[1])value theorem. (10[3])A function has (10[3])this property if (10[1])it equals (10[4]-5[1])its limit at (10[3])every (10[1])point. For (10[1])10 (10[2])points, (10[1])name this property (10[1])of (10[1])a function that can (10[1])be defined informally as being able to draw (10[1])its (10[1])graph without taking the (10[1])pen off (10[1])the (10[6]0[1])paper. ■END■