Results 1 to 6 of 6

Math Help - fi nite intersection property

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    47

    fi nite intersection property

    Hey, I am really stuck on a question so if anyone can help me I would be very grateful.

    Show that the set of finite unions of closed intervals \{ \cup^n_{i=1} [x_i,y_i] : 0 \le x_i \le y_i \le 1 n \in \mathbb{N} \} in X = [0,1] has the f.i.p.


    I know that for a collection of sets to have the finite intersection property means that each nonempty finite subcollection of these sets has a nonempty intersection.

    But I am unsure how to do this question and how to set it out.

    Thanks in advance for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Nguyen View Post
    Hey, I am really stuck on a question so if anyone can help me I would be very grateful.

    Show that the set of finite unions of closed intervals \{ \cup^n_{i=1} [x_i,y_i] : 0 \le x_i \le y_i \le 1 n \in \mathbb{N} \} in X = [0,1] has the f.i.p.


    I know that for a collection of sets to have the finite intersection property means that each nonempty finite subcollection of these sets has a nonempty intersection.

    But I am unsure how to do this question and how to set it out.

    Thanks in advance for any help.

    As you defined that set of intervals the claim is false: for example, it could be that two of the

    intervals are [1,\,1/3]\,,\,[1/2,\,2/3] , whose intersection is finite...

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2010
    Posts
    47
    Quote Originally Posted by tonio View Post
    As you defined that set of intervals the claim is false: for example, it could be that two of the

    intervals are [1,\,1/3]\,,\,[1/2,\,2/3] , whose intersection is finite...

    Tonio

    Thanks for your reply but I still don't understand how to show that the set of finite unions has a f.i.p. Sorry for being a pain.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,708
    Thanks
    1638
    Awards
    1
    Quote Originally Posted by Nguyen View Post
    Show that the set of finite unions of closed intervals \{ \cup^n_{i=1} [x_i,y_i] : 0 \le x_i \le y_i \le 1 n \in \mathbb{N} \} in X = [0,1] has the f.i.p.
    Quote Originally Posted by Nguyen View Post
    I still don't understand how to show that the set of finite unions has a f.i.p. Sorry for being a pain.
    Of course you do not, Because as originally posted the statement is false.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,790
    Thanks
    1531
    Quote Originally Posted by tonio View Post
    As you defined that set of intervals the claim is false: for example, it could be that two of the

    intervals are [1,\,1/3]\,,\,[1/2,\,2/3] , whose intersection is finite...
    tonio meant "empty" here.

    Tonio
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,962
    Thanks
    349
    Awards
    1
    Quote Originally Posted by HallsofIvy View Post
    tonio meant "empty" here.
    The intersection of [1/3, 1] and [1/2, 2/3] is [1/2, 2/3] isn't it?

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mean Value Property Implies "Volume" Mean Value Property
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 16th 2011, 08:13 PM
  2. set property help
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: June 28th 2010, 04:09 AM
  3. Replies: 2
    Last Post: October 19th 2009, 02:47 AM
  4. Property tax??
    Posted in the Business Math Forum
    Replies: 1
    Last Post: September 14th 2008, 07:33 PM
  5. property
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 12th 2008, 08:32 PM

Search Tags


/mathhelpforum @mathhelpforum