Thread: 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 an open subset of with respect to the Sorgenfrey topology?
Provide a proof for your answer.


(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).

This webpage may be useful.

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.

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 .
That question asks if , the rationals, is open in with the Sorgenfrey topology.

I do not think there is much hope of helping you.

Agreed.

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?

erm... no. Or maybe yes? Any chance you'd like to explain it to me?

What is the standard basis of the Sorgenfrey topology on R?