# Math Help - normal topological space

1. ## 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.

2. 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

3. Originally Posted by swallenberg
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.
Originally Posted by facenian
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.

It's clearly Hausdorff, right? Since if $x\ne y$ then WLOG $x and so $[x,\tfrac{x+y}{2}),(\tfrac{x+y}{2},y]$ are disjoint basic open sets containing them.