Is the definition of a closed set an implication?

My understanding of the definition is this:

OPEN: For a set U in R. U is open if for all x in U there exists an m>0 s.t. (x-m, x+m) is also in U.

CLOSED: For a set F=R\U. If F is open then U is closed.

So if I find that F is not open, does that mean that U is not closed?

Thanks a bunch!