# Sorgenfrey stuff

• May 4th 2011, 08:08 AM
MathSucker
Sorgenfrey stuff
I am taking an introductory Topology course. I am having a completely impossible time with it.

If somebody could explain in simple terms what this means, I would greatly appreciate it:

Is \$\displaystyle Q\$ an open subset of \$\displaystyle R\$ with respect to the Sorgenfrey topology?

(I am not trying to get you to do my homework. This is a question from a previous exam, and I am just trying to figure out how to do these questions).
• May 4th 2011, 08:42 AM
Plato
• May 4th 2011, 09:01 AM
MathSucker
I always look at wikipedia, but I find it's unhelpful unless you have some knowledge of the subject. I have limited examples in my notes and zero worked solutions, so I'm always lost.
• May 4th 2011, 09:30 AM
Plato
Quote:

Originally Posted by MathSucker
I always look at wikipedia, but I find it's unhelpful unless you have some knowledge of the subject. I have limited examples in my notes and zero worked solutions, so I'm always lost.

Are you saying that you have little working knowledge of Sorgenfrey topology?
If that is the case, I do not think there is much hope of helping you.
In Sorgenfrey topology, the basic open sets look like \$\displaystyle [a,b)\$.
That question asks if \$\displaystyle \mathbb{Q}\$, the rationals, is open in \$\displaystyle \mathbb{R}\$ with the Sorgenfrey topology.
• May 4th 2011, 09:40 AM
MathSucker
Quote:

I do not think there is much hope of helping you.
Agreed.
• May 4th 2011, 11:39 AM
Tinyboss
Every open set contains a basis element (regardless of the topology or which basis you choose to consider). Does the standard basis of the Sorgenfrey topology have any elements that contain only rationals?
• May 5th 2011, 12:30 AM
MathSucker
erm... no. Or maybe yes? Any chance you'd like to explain it to me?
• May 5th 2011, 05:14 AM
Tinyboss
What is the standard basis of the Sorgenfrey topology on R?