Proving Discrete Topology: Topology Problem on Set of Integers

[mathshelp]

Homework Statement

Let U be a topology on the set Z of integers in which every infinite subset
is open. Prove that U is the discrete topology, in which every subset is open.

Homework Equations

Just the definition of discrete topology

The Attempt at a Solution

I'm not sure where to start!

 

[latentcorpse]

yeah i think that this is the same method used in the other thread someone else made with the second part of this question. find two infinite subsets of Z that intersect at a single point. then by doing this for every element of Z you can show that every 1 element subset of Z is open. then u can take arbitrary unions to show every possible subset of Z is open and hence U is the power set of Z.