Results 1 to 2 of 2

Math Help - Compact subset problem

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Compact subset problem

    Define A = {(x,y) in R^2 : x^2+y^2 <= 4 and y >= x} U {(2,2)}.

    a) Is A open?
    b) Is A closed?
    c) What is int A?
    d) What is ext A?
    e) What is bd A?
    f) Is A bounded?
    g) Is A a compact subset of R^2?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by tttcomrader View Post
    Define A = {(x,y) in R^2 : x^2+y^2 <= 4 and y >= x} U {(2,2)}.

    a) Is A open?
    No, there are points in A for which every neighbourhood of the point contains
    points not in the set.

    b) Is A closed?
    Yes, it contains all its limit points

    c) What is int A?
    (check these from here on)

    {(x,y): x^2+y^2<4, and y>x}

    d) What is ext A?
    {(x,y): x^2+y^2>4, or y<x}

    e) What is bd A?
    {(x,y): x^2+y^2=4, and y>x}U {(x,y): y=x and x in [-sqrt(2),sqrt(2)]} U {(2,2)}

    f) Is A bounded?
    yes

    g) Is A a compact subset of R^2?
    It is closed and bounded and so compact.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Closed subset of sequentially compact set is sequentially compact.
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 13th 2011, 01:25 PM
  2. inf and sup of a compact subset of R
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: February 28th 2010, 08:04 PM
  3. Examples of non-compact space with infinite subset
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: January 17th 2010, 10:44 AM
  4. Continuous function on a compact subset of R
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 5th 2009, 01:12 PM
  5. compact subset of R
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: March 3rd 2009, 02:56 PM

Search Tags


/mathhelpforum @mathhelpforum