Limit points and exterio points Quick quesiton

[Buri]

Is the following true?

X\lim(A) = ext(A), where A is a subset of a metric space X.

I think I've found a proof, but I don't feel very secure about it. So could someone just tell me if this is a correct assertion? What I'm trying to prove is that lim(A) is closed.

Thanks

 

[arkajad]

Take A being a one-point set. What is lim(A)? What is ext(A)?

 

[Buri]

I hate isolated points! lol Thanks