Results 1 to 4 of 4

Math Help - Closure, Interior and limit points of finite compliment topology question

  1. #1
    Banned
    Joined
    Apr 2009
    Posts
    5

    Closure, Interior and limit points of finite compliment topology question

    Hey

    I was wondering if someone could help me out with the following question.

    Let U be any open set in the finite complement topology on \Re.

    (a)Describe the Cl(U), Int(U) and \mathfrak{d}(U)

    (b) What is the set of limit points of U
    Last edited by mr fantastic; May 22nd 2009 at 04:19 AM. Reason: Restored original question deleted by OP
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    394
    Quote Originally Posted by monkey.brains View Post
    Hey

    I was wondering if someone could help me out with the following question.

    Let U be any open set in the finite complement topology on \Re.

    (a)Describe the Cl(U), Int(U) and \mathfrak{d}(U)

    (b) What is the set of limit points of U
    (a) Cl(U) = R, Int(U) = U,
    \mathfrak{d} (U) = \bar{U} \cap \overline{R\setminus U},
    Since U is an open set, \mathfrak{d}(U) = \overline{R\setminus U} = R \setminus U.
    (b)The limit points of U are all points in R.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Apr 2009
    Posts
    5
    Quote Originally Posted by aliceinwonderland View Post
    (a) Cl(U) = R, Int(U) = U,
    \mathfrak{d} (U) = \bar{U} \cap \overline{R\setminus U},
    Since U is an open set, \mathfrak{d}(U) = \overline{R\setminus U} = R \setminus U.
    (b)The limit points of U are all points in R.

    hey could you please clarify what does the line over R minus U means??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,646
    Thanks
    1596
    Awards
    1
    Quote Originally Posted by monkey.brains View Post
    hey could you please clarify what does the line over R minus U means??
    Often \overline{A} stands for the closure of A.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find the closure of A in the co-finite topology
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 13th 2011, 11:55 AM
  2. [SOLVED] Finite Compliment Topology
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: March 9th 2011, 11:46 AM
  3. limit points of Aintersect B, closure of (AintersectB)
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: November 4th 2010, 04:26 PM
  4. interior of set closure differnet from interior of the same set?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 17th 2009, 11:13 AM
  5. finite compliment and discrete topology question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 17th 2009, 12:54 PM

Search Tags


/mathhelpforum @mathhelpforum