Thread: Topological Groups

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.

Originally Posted by Turloughmack

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.

I fully answered one of your questions and ask you to show work on the other, but instead you just repost it.

This is, as Plato would say, not a tutoring service. Let's see some work!