# Set of integers

1. Oct 12, 2008

### julia89

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

is the set of integers open or closed
2. Relevant equations

3. The attempt at a solution

I thought not closed
open because R/Z=Union of open intervals
like ....U(-1,0)U(0,1)U.....

2. Oct 12, 2008

### morphism

You got it backwards!

3. Oct 12, 2008

### HallsofIvy

Staff Emeritus
With what topology? The topology inherited from the reals? (That is, the metric topology with d(m,n)= |m- n|.)

Morphism's point is that since R\Z is a union of a union of open intervals, The complement of Z is open and so Z itself is ?

However, don't think that "open" or "closed" are all the options. It is possible for a set to be neither open nor closed. It is even possible for a set to be both open and closed.

4. Oct 13, 2008

### julia89

ow sorry I switched open and closed
I meant that it was a closed set and not open

5. Oct 13, 2008

### morphism

Yes, then that's right. The set is closed and not open.