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**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Normal space goes to Normal space.

Loading...

Similar Threads - Normal space goes | Date |
---|---|

I Coordinate systems vs. Euclidean space | Dec 4, 2017 |

A Degree of Gauss normal map | Nov 30, 2016 |

A Normal velocity to the surface in Spherical Coordinate System | May 17, 2016 |

Principal normal and curvature of a helix | May 17, 2015 |

Geodesic curvature, normal curvature, and geodesic torsion | Mar 3, 2014 |

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