Hi All, I can't see how the following is proved. Given two topological space (X, T), (Y, U) and a function f from X to Y and the following two statements. 1. f is continuous, i.e. for every open set U in U, the inverse image f-1(U) is in T 2. For every convergent filter base F -> x, the induced filter base f [[F]] -> f(x) it is claimed that statement 1 and statement 2 are equivalent, i.e. 1 if and only if 2 I can prove 1 -> 2 but how do i prove 2 -> 1 thanks a lot !