Results 1 to 2 of 2

Math Help - Set compact and connected

  1. #1
    Member thaopanda's Avatar
    Joined
    Sep 2009
    From
    Worcester, Massachusetts
    Posts
    85

    Set compact and connected

    Show that the set S := { (x,y) \in R^2 : x^2 + y^2 = 1} is compact and connected.

    To show it is compact, I would need to find a finite open cover for S... I think... but I really have no idea what that means

    And for it being connected, that means S cannot be written as two disjoint open sets, but again, I don't know how to prove that, since our professor only just introduced the topic....

    thanks for any help you can provide!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    The Heine-Borel Theorem states that any closed and bounded set in \mathbb{R}^n is compact.

    As for connectedness, there is a theorem that states that if you have a continuous function f that maps E\subset X\longrightarrow Y, and E is connected, then f(E) is also connected.

    That should get you going in the right direction.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. compact connected
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 6th 2010, 07:27 AM
  2. Proof that union of two connected non disjoint sets is connected
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 27th 2009, 08:22 AM
  3. Proving connected/compact
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: November 30th 2008, 12:11 PM
  4. Replies: 1
    Last Post: April 18th 2008, 07:19 AM
  5. Images of Compact and Connected Sets
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 13th 2006, 01:35 PM

Search Tags


/mathhelpforum @mathhelpforum