Results 1 to 3 of 3
Like Tree2Thanks
  • 1 Post By HallsofIvy
  • 1 Post By Plato

Thread: How to determine if a point is a closure point of a set

  1. #1
    Newbie
    Joined
    Feb 2018
    From
    United Kingdom
    Posts
    1

    How to determine if a point is a closure point of a set

    How to determine if for e.g. (3,0) is a closure point of a set C
    where C=A ∩ B
    Where A=1
    x^2+y^2≤9
    B=IxI>1

    How would I start something like this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,860
    Thanks
    3071

    Re: How to determine if a point is a closure point of a set

    A point, P, is a closure point of set S (is in the closure of S) if and only if every open neighborhood of P contains a point of X. Here, (3, 0) is in set B and $3^2+ 0^2= 9$ so, for any $\epsilon> 0$, $(3- \epsilon, 0)$ is in C.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,880
    Thanks
    2890
    Awards
    1

    Re: How to determine if a point is a closure point of a set

    Quote Originally Posted by asrm View Post
    How to determine if for e.g. (3,0) is a closure point of a set C
    where C=A ∩ B
    Where A=1≤x^2+y^2≤9
    B=IxI>1 How would I start something like this?
    Denote the closure of $X$ by $\overline{X}$
    Using that definition it is clear that $X\subseteq\overline{X}$. In this case is it true that $(3,0)\in A\cap B~?$
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Determine a point on f(x)
    Posted in the Calculus Forum
    Replies: 8
    Last Post: Apr 9th 2017, 02:39 AM
  2. Determine the Point(s)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Oct 12th 2015, 03:00 PM
  3. Determine the Point(s)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 12th 2015, 02:58 PM
  4. Replies: 6
    Last Post: Mar 28th 2010, 01:10 PM
  5. Closure and accumlation point problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Sep 20th 2008, 12:36 PM

Search Tags


/mathhelpforum @mathhelpforum