1. The problem statement, all variables and given/known data Let X be a set and p is in X, show the collection T, consisting of the empty set and all the subsets of X containing p is a topology on X. 2. Relevant equations? A topology T on X is a collection of subsets of X. i) X is open ii) the intersection of finitely many open sets is open iii) the union of any collection of open sets is an open set. 3. The attempt at a solution How do I know that X is open. Maybe open doesn't mean the same thing as an open set on the reals. if X is open. And If I take an intersection of a finite number of sets in T i will get something in T so by definition It will produce an open subset in T. And all my intersections will contain P because P is in every set. for iii) If I take a union of all the subsets in T I will produce a subset in T containing p. I could not produce something outside of T because i started with sets that were part of T.