Is Cos(x) a Closed Function in R?

[emptyboat]

I think cos(x) is closed function in R.
But I heard that cos(x) is not closed function in R.
What do I choose closed set A in R, cos(A) is not closed in R?
Help...

 

[quasar987]

Consider for instance the set A := \{2n\pi-1/n: n\in\mathbb{N}\}. It is closed, but cos(A) does not contain its limit point 1.

 

[emptyboat]

Thank you, friend. I tried closed intervals...