Results 1 to 4 of 4

Math Help - Show that I^n and S^n are path-connected?

  1. #1
    Junior Member
    Joined
    Feb 2011
    Posts
    52

    Show that I^n and S^n are path-connected?

    Show that I^n (unit cube) and S^n (n > 0) are both path-connected by constructing a path.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21

    Re: Show that I^n and S^n are path-connected?

    Quote Originally Posted by Borkborkmath View Post
    Show that I^n (unit cube) and S^n (n > 0) are both path-connected by constructing a path.
    The cube you can literally just do a piecewise linear map (go down the appropriate amount and over the appropriate amount), for \mathbb{S}^n just paramaterize it with two charts and go from there. Try this and report back if you have any issues.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2011
    Posts
    52

    Re: Show that I^n and S^n are path-connected?

    What do you mean by paramaterize it with two charts?
    Sorry, if my question is silly
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21

    Re: Show that I^n and S^n are path-connected?

    Quote Originally Posted by Borkborkmath View Post
    What do you mean by paramaterize it with two charts?
    Sorry, if my question is silly
    No, I'm sorry, it's not a silly question, and you really need more than two charts theoretically. But, even that's just stupid. If it's on a sphere, just think about a great circle which contains the two points and take either of the paths induced from that.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Show that I^n and S^n are path-connected?
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: November 29th 2011, 06:00 PM
  2. Path connected
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 19th 2011, 08:51 PM
  3. Every path-connected metric space is connected
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 13th 2011, 07:31 AM
  4. Connected and Path Connected
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 14th 2010, 01:28 PM
  5. Replies: 1
    Last Post: April 18th 2008, 08:19 AM

Search Tags


/mathhelpforum @mathhelpforum