- #1

- 2,552

- 3

## Homework Statement

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.

## Homework 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.

## 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.