Results 1 to 4 of 4

Thread: 2 questions in TOPOLOGY

  1. #1
    Junior Member
    Joined
    Jan 2007
    Posts
    48

    2 questions in TOPOLOGY

    please:
    I need your help in these 2 Qs:
    the picture2 questions in TOPOLOGY-untitled.gif
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,741
    Thanks
    2812
    Awards
    1
    The first problem is proved in two steps.
    First, If $\displaystyle B$ is a compact set and $\displaystyle p\notin B$ then there are two disjoint open sets such $\displaystyle B\subset G~\&~p\in H$.

    Second, each point in $\displaystyle A$ is not in $\displaystyle B$.
    If $\displaystyle a\in A$ use part one to get disjoint open sets $\displaystyle G_a~\&~H_a$.
    The compactness of $\displaystyle A$ gives a finite collection of each.
    The intersection of the $\displaystyle G_x's $ is open and contains $\displaystyle B$.

    Problem #2. Use the co-finite topology to show it is false.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2007
    Posts
    48
    thank u
    but could u please clear the second question more
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    22
    Quote Originally Posted by rqeeb View Post
    thank u
    but could u please clear the second question more
    He's suggesting that you take $\displaystyle \mathbb{R}$ with the cofinite topology. The important thing being that the resulting top. space isn't first countable.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Questions on topology
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Jul 7th 2011, 12:24 AM
  2. Topology questions
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: May 2nd 2010, 08:31 PM
  3. Topology questions
    Posted in the Differential Geometry Forum
    Replies: 12
    Last Post: Mar 2nd 2010, 07:08 PM
  4. Topology questions
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: Mar 2nd 2010, 06:50 AM
  5. questions in topology
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Jan 2nd 2010, 06:39 AM

Search Tags


/mathhelpforum @mathhelpforum