Can anybody help me with this question

Given topological groups X and Y and homomorphism f:X->Y, verify the following are equivalent:

(a) f is an open map

(b) for each neighborhood N of e(x), f(N) is a neighborhood of e(y)

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

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

I already know that f is continuous which implies f is continuous at the identity e(x) of x