Results 1 to 3 of 3

Math Help - Closed, open, int, adh and boundary

  1. #1
    Junior Member
    Joined
    Mar 2011
    Posts
    49

    Closed, open, int, adh and boundary

    Verify if the following sets are closed, open and find \text{int}\, A,\overline A,\partial A and the set of accumulation points. (Does the last set have a name?)

    a) A=\{(x,y)\in\mathbb R^2|y>x\}

    b) If a\in\mathbb R^n, A=\{x\in\mathbb R^n|x\cdot a=1\}

    c) A=\displaystyle\overline{B}\left( \left( \frac{3}{4},0 \right),\frac{1}{4} \right)\cup \bigcup\limits_{k=2}^{\infty }{B\left( \left( \frac{3}{{{2}^{k+1}}},0 \right),\frac{1}{{{2}^{k+1}}} \right)}.

    I have the definitions but I'm not sure how to proceed.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32
    There is a link between continuity of maps and open and closed sets.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    I believe that the set of limit points of A can be called the derived set of A, and is sometimes denoted by A'.

    The boundary of the first set is y=x. Note that none of the boundary points are in the set. What does this tell you about the set being open or closed?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove a set is open iff it does not contain its boundary points
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 24th 2011, 06:16 PM
  2. Replies: 5
    Last Post: September 4th 2010, 08:58 AM
  3. open and closed set
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: July 18th 2010, 12:12 PM
  4. 1D wave equation open boundary
    Posted in the Math Software Forum
    Replies: 16
    Last Post: July 9th 2010, 09:58 AM
  5. how to prove the boundary of a set is closed?
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: November 17th 2009, 07:49 PM

Search Tags


/mathhelpforum @mathhelpforum