here's the question:(adsbygoogle = window.adsbygoogle || []).push({});

prove that if: f:X->Y is onto Y, closed (i.e return closed sets from given closed sets in X) and continuous then if X is Normal (satisfy axioms: T1 and T4) then also Y is Normal.

Now I've showed that if X is T1 then Y is T1, but I'm having difficulty with T4.

here's what I did:

let F,G be disjoint closed sets of Y, then by continuity f^-1(F) and f^-1(G) are closed in X, and they are disjoint because: f^-1(FחG)=f^-1(G)חf^-1(F), now because X is T4 we have neighbourhoods of f^-1(F) and f^-1(G) which are disjoint, now I need to show that also F a G have this property, I guess I need to use the onto feature, but how?

any hints?

**Physics Forums - The Fusion of Science and Community**

# Normal space goes to Normal space.

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

- Similar discussions for: Normal space goes to Normal space.

Loading...

**Physics Forums - The Fusion of Science and Community**