1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Topology question

  1. Nov 1, 2006 #1
    Prove: If p:X->Y is a quotient map and if Z is a locally compact Hausdorff space, then the map m: p x i : X x Z -> Y x Z is a quotient map.

    Note: i is the identity map on Z i assume. There is a few lines of hints talking about using the tube lemma and saturated neighborhoods which i dont feel like writing at the moment (see Munkres p.186). The main problem i have have with this is why not say: p x i (U x V) = p(U) x i(V), so (p x i)^-1 (U x V) = p^-1(U) x i^-1(V) (is this not true?). Because if it is true then the result seems trivial since p is a quotient map and the identity does nothing to change the openness of V. What am i missing?
  2. jcsd
  3. Nov 2, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    What does it mean for p x i to be a quotient map? You can use what you've done to prove that p x i is continuous, but you would need to do more to prove that it's a quotient map.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Topology question
  1. Topology question (Replies: 0)

  2. Topology Question (Replies: 3)

  3. Topology Question (Replies: 4)

  4. Topology question (Replies: 2)

  5. Topology question (Replies: 5)