Results 1 to 2 of 2

Math Help - Topology

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    1

    Exclamation Topology

    In a more involved proof, I am getting caught up on this single step.

    Let f: X --> R^(2k) be an immersion and F: T(X) --> R^(2k), where T(X) is the tangent bundle, and F(x,v) = df_x (v) (it is the differential of F at x on the vector v.) Let "a" be a regular value of F. Show that F inverse of a is a finite set.

    Any suggestions on how to show it is finite? Thanks a lot.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Rebesques's Avatar
    Joined
    Jul 2005
    From
    At my house.
    Posts
    527
    Thanks
    7
    First of all, X should be compact. Note that F^{-1}(a) is closed in X. Also, as a is a regular value, F must be one to one over a neighbourhood of each element in F^{-1}(a).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Order topology = discrete topology on a set?
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: August 6th 2011, 11:19 AM
  2. a topology such that closed sets form a topology
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: June 14th 2011, 04:43 AM
  3. Show quotient topology on [0,1] = usual topology on [0,1]
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: November 5th 2010, 04:44 PM
  4. discrete topology, product topology
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: December 13th 2008, 02:19 PM
  5. discrete topology, product topology
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: December 7th 2008, 01:01 PM

Search Tags


/mathhelpforum @mathhelpforum