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.