Urgent answer required!

Q. Given topological groups X & Y, and homorphism f:X->Y, verify that the following are equivalent:

(a) f is an open map

(b) for each nhd N of e(x), f(N) is a nhd or e(y), e(x) is the identity

(c) for each open nhd N of e(x), f(N) is a nhd of e(y)

(d) for each open nhd N of e(x), f(N) is an open nhd of e(y)

I know some of these are obvious but whats obvious to one person isn't always obvious to another.