Results 1 to 5 of 5

Math Help - Demonstration of that the union of manifolds is not a mainfold

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    22

    Demonstration of that the union of manifolds is not a mainfold




    Hello.
    I was looking for that demonstration, and I know how to start: As they aren't contain in each other I have to take a point in each one that it is not in the other one. So they (the points) will be in the union of both of the mainfolds. So I have to proove that the half point of them is not in the union. That's all.

    Thank you so much (I hope you have understood my English, I am from Spain)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,545
    Thanks
    780
    This question is more about topology than logic. You should send a private message to Plato or another moderator and ask him to move the thread. Or perhaps you can post this in the Analysis, Topology and Differential Geometry forum and make a note about it here.

    If this question comes from a course in logic (and not topology), then please let us know. In this case, a definition of a manifold would be useful.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Mar 2010
    From
    Beijing, China
    Posts
    293
    Thanks
    23
    The line R is a manifold. But the union of two crossing lines is not.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    You could also consider the disjoint union of two manifolds of different dimensions.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Lolyta View Post



    Hello.
    I was looking for that demonstration, and I know how to start: As they aren't contain in each other I have to take a point in each one that it is not in the other one. So they (the points) will be in the union of both of the mainfolds. So I have to proove that the half point of them is not in the union. That's all.

    Thank you so much (I hope you have understood my English, I am from Spain)
    You could take the union of a zero-dimensional submanifold of \mathbb{R}^2 and \mathbb{S}^1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ok, I know manifolds. What's next?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 15th 2011, 12:50 AM
  2. conclude that the closure of a union is the union of the closures.
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 13th 2011, 06:50 PM
  3. Disjoint union of manifolds
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 4th 2010, 11:43 PM
  4. Mobius n-manifolds within Complex n manifolds
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: January 20th 2010, 07:15 AM
  5. [SOLVED] 1-manifolds
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 19th 2008, 02:56 PM

Search Tags


/mathhelpforum @mathhelpforum