Results 1 to 3 of 3

Math Help - normal topological space

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    13

    normal topological space

    Hello!

    Ok, here it goes:

    T={[x,y); x,y belong to R and x<y} (R = the set of real numbers)

    Show that (R,T) is normal.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Feb 2010
    Posts
    37
    I don't understand the queston because T doesn't seem to be a topology may be T is the base for a topology on R
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by swallenberg View Post
    Hello!

    Ok, here it goes:

    T={[x,y); x,y belong to R and x<y} (R = the set of real numbers)

    Show that (R,T) is normal.
    Quote Originally Posted by facenian View Post
    I don't understand the queston because T doesn't seem to be a topology may be T is the base for a topology on R
    It's supposed to be the topology for which that is a base, it is usually called the half-open interval topology or the Sorgenfrey line.

    So, how much topology do you know? How much do you know about this specific topology?

    Where's your work?

    It's clearly Hausdorff, right? Since if x\ne y then WLOG x<y\implies x<\frac{x+y}{2}<y and so [x,\tfrac{x+y}{2}),(\tfrac{x+y}{2},y] are disjoint basic open sets containing them.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A is a subset of a topological space X
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: August 28th 2011, 02:40 PM
  2. Topological space
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 2nd 2010, 09:23 PM
  3. retract in a topological space
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 23rd 2009, 11:51 PM
  4. a topological space
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: March 8th 2009, 04:39 AM
  5. Proof in a topological space
    Posted in the Advanced Math Topics Forum
    Replies: 22
    Last Post: January 24th 2006, 08:50 AM

Search Tags


/mathhelpforum @mathhelpforum