Results 1 to 2 of 2

Math Help - Balls connected in R^n

  1. #1
    Junior Member
    Joined
    Feb 2008
    Posts
    63

    Balls connected in R^n

    Show that the open balls and closed balls in the standard metric on \mathbb{R}^n are connected in \mathbb{R}^n
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Andreamet View Post
    Show that the open balls and closed balls in the standard metric on \mathbb{R}^n are connected in \mathbb{R}^n
    note that S \subseteq \mathbb{R}^n is path-wise connected, implies that it is connected. thus, you have the desired result, if you can show that open balls and closed balls are path-wise connected.

    note that any two points in an open or closed ball can be connected by a straight line that is contained in the ball
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 7th 2011, 05:58 PM
  2. Every path-connected metric space is connected
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 13th 2011, 07:31 AM
  3. a basket contains 5 red balls, 3 blue balls, 1 green balls
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: May 28th 2010, 03:39 AM
  4. Proof that union of two connected non disjoint sets is connected
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 27th 2009, 09:22 AM
  5. Replies: 1
    Last Post: April 18th 2008, 08:19 AM

Search Tags


/mathhelpforum @mathhelpforum