Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By topsquark

Thread: Show that set is not open nor closed

  1. #1
    Newbie
    Joined
    Jan 2017
    From
    Netherlands
    Posts
    9

    Show that set is not open nor closed

    I have a set I = {x from R2 : x1<1 v x2>=2}
    I have to show it isn't neither open or closed.

    Can I do this?:
    x1<1then I can choose for that point an open disc of radius r = 1-x1
    Every point y in that disc has 2x11<y1<1, so y1<1, so every point in the disk satisfies the first inequality so this is open

    But if I do the same for x2, then I get 2<y1, so this isn't the same as x2>=2. Can I conclude that it isn't open? I can also say that if x2=2 you cannot say that there is an open ball in I with center z and radius r. So it isn't open.

    What have I going to do?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2009
    Posts
    349
    Thanks
    48

    Re: Show that set is not open nor closed

    I would recommend reviewing the formal definitions of open and closed.

    Consider the analogue case of [0,1) in R (with the usual topology on the reals). If you can show it's not open nor closed, then showing that set I is not open nor closed should be similar.
    Last edited by MacstersUndead; Jan 31st 2017 at 06:01 AM. Reason: thanks topsquark. addendum
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,019
    Thanks
    687
    Awards
    1

    Re: Show that set is not open nor closed

    The whole open/closed question bring to mind topology. I'm not sure what kind of set structures you are using in DG. There is a topology (the name escapees me at the moment) where [0, 1) is open. Or are we assuming we are using the "usual topology" on the reals?

    -Dan
    Thanks from MacstersUndead
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,198
    Thanks
    2626
    Awards
    1

    Re: Show that set is not open nor closed

    Quote Originally Posted by Cyn1 View Post
    I have a set I = {x from R2 : x1<1 v x2>=2}
    I have to show it isn't neither open or closed.
    Can I do this?: x1<1then I can choose for that point an open disc of radius r = 1-x1
    Every point y in that disc has 2x1−1<y1<1, so y1<1, so every point in the disk satisfies the first inequality so this is open.
    The point $\mathcal{P}: (1,2)\notin\mathcal{I}$. Now if $\varepsilon >0$ then any ball $\mathscr{B}_{\varepsilon}(\mathcal{P})$ contains points in $\mathcal{I}$ and points not in $\mathcal{I}$, therefore $\mathcal{P}$ is a boundary point of $\mathcal{I}$ not in $\mathcal{I}$. That is enough to show that $\mathcal{I}$ is neither open nor closed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Show A neither open nor closed
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: Aug 27th 2011, 09:15 PM
  2. Show the set of rational numbers Q is neither open nor closed.
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Feb 23rd 2011, 08:18 PM
  3. Show these intervals are open and closed sets.
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: Feb 17th 2011, 02:59 AM
  4. Set in R^2 which is neither open nor closed.
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Nov 3rd 2010, 11:46 PM
  5. open and closed set
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Jul 18th 2010, 12:12 PM

Search Tags


/mathhelpforum @mathhelpforum