Let X and Y be two sets and let f : XY be a function. If F is a o-algebra over the subsets of Y and G = { A |3 BE F such that f-(B) = A } , does G form a o-algebra of subsets of X ? Note that f-(N) is the notation used for the pre-image of set N under the function f for some N CY. That is, f-'(N) = {r X]f(x) N} for some N CY. %3D