# Topology problem

1. Oct 9, 2009

### mathshelp

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Just the definition of discrete topology

3. The attempt at a solution

I'm not sure where to start!

2. Oct 9, 2009

### 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.