Set of Integers: Open or Closed?

[julia89]

Homework Statement

is the set of integers open or closed

Homework Equations

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...

 

[morphism]

You got it backwards!

 

[HallsofIvy]

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.

 

[julia89]

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

 

[morphism]

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