I'm trying to teach myself topology from Munkres' book (first edition, it's over 30 years old!) and it's going very slowly. I'm having some difficulty proving the following:
Let be a collection of topologies on . Show that there is a unique smallest topology containing all the collections , and a unique largest topology contained in all .
This is part b in a three part problem. The first part was to prove that if is a collection of topologies on that is a topology on , which I was able to do. So, imagine that result will be useful in what I'm trying to prove here.