Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Properties of Differentials, Smooth Manifolds.

  1. Feb 24, 2013 #1
    I'm reading the second edition of John M. Lee's Introduction to Smooth Manifolds and he has a proposition that I'd like to understand better

    Let M, N, and P be smooth manifolds with or without boundary, let F:M→N and G:N→P be smooth maps and let p[itex]\in[/itex]M

    Proposition: TpF : TpM → TF(p) is linear

    ok I know that v[itex]\in[/itex]TpM means that

    v:C(M)→ℝ is a derivation and that TpM is a vector space.

    Does this mean that the image of (av+bw) under TpF where v,w [itex]\in[/itex] TpM and a,b [itex]\in[/itex] ℝ

    is aTpF(v) + bTpF(w) which means TpF is linear?
     
  2. jcsd
  3. Feb 24, 2013 #2
    Yes, that's what it means.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Properties of Differentials, Smooth Manifolds.
Loading...