Results 1 to 2 of 2

Math Help - Topology of the Reals

  1. #1
    Newbie Chief65's Avatar
    Joined
    Sep 2008
    From
    Denver
    Posts
    18

    Topology of the Reals

    I'm stuck on some proofs, wondering if anyone could lend a hand.
    Let S be a subset of R

    a) Prove: bd (S) = (cl S) ∩ [cl (R\S)]

    b) Prove: bd (S) is a closed set

    *bd (S) is a boundary point of S. cl (S) is a closure of S. (R\S) is S^c (compliment of S)*
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    394
    Quote Originally Posted by Chief65 View Post
    I'm stuck on some proofs, wondering if anyone could lend a hand.
    Let S be a subset of R

    a) Prove: bd (S) = (cl S) ∩ [cl (R\S)]

    b) Prove: bd (S) is a closed set

    *bd (S) is a boundary point of S. cl (S) is a closure of S. (R\S) is S^c (compliment of S)*
    (a) is simply a definiton of a boundary of S in R.
    (b) An intersection of closed sets is a closed set. Both (cl S) and cl (R\S) are closed sets, so bd(S) is a closed set.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. a topology such that closed sets form a topology
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: June 14th 2011, 05:43 AM
  2. Show quotient topology on [0,1] = usual topology on [0,1]
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: November 5th 2010, 05:44 PM
  3. Replies: 1
    Last Post: August 23rd 2010, 09:23 AM
  4. Replies: 1
    Last Post: May 14th 2010, 02:53 AM
  5. Topology of the Reals proofs
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 12th 2009, 03:30 PM

Search Tags


/mathhelpforum @mathhelpforum