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).
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.
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?