Is the set of positive real numbers open, closed, or neither

[felvt]

I'm supposed to decide if the set of positive real numbers {x ? R : x>0} is open, closed, or neither. I believe it is open. I am not sure if 0 is a limit point of this set though, which would mean it is not closed.

 

[stapel]

What is the definition of a "limit point" of a set?

Thank you!

Eliz.

 

[felvt]

Re: Open and Closed sets

Ah, found it, x is a limit point of the set if every ?-nbd contains at least one point of the set other than x. So 0 is a limit point and the set is not closed since it doesn't contain 0.