Openness of subsets of the integers.

[jamesstarmer]

1. What are all the open subsets of the subspace Z of R.



2. Homework Equations : def of openness



3. I think the solution is all the subsets of Z, but I can't see how, for example you can say the subset of Z: {1} has a B(1,r) with r>0 is contained in {1}.

Thanks for any help.

 

[HallsofIvy]

You don't. It is easy to show that every singleton set is closed. But only finite intersections of closed sets are closed so only complements of finite sets are open.