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.
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.
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