Prove that Ti2I Fi is a filter on X b Let fGn n 2 Ng be a c

Prove that Ti2I Fi is a filter on X.

b) Let fGn : n 2 Ng be a collection of filters on a nonempty set X, such that for any natural number

n, Gn µ Gn+1. Prove that

S

n2N Gn is a filter on X. [10 Pts]

(c) Let X and Y be nonempty sets. Let f : X ! Y be a function. Let B be a filter basis on X. Prove

that f(B) = ff(B) : B 2 Bg is filter basis on Y .

Solution