A subset U CR is called open if it has the property Ve e U 36 > 0 Va' e R: 2 - a'| < 8 = ' e U. (In particular, O is considered open.) Given a e R, then any open subset U containing a is called an open neighborhood of a. Show that if f: X R is a function, then lim, va f(a) = l if and only if the following condition holds: for every open neighborhood V of e there exists an open neighborhood U of a such that f(U - {a}) C V.