# general topology – Topologies on \$mathbb{R}\$

I have found this in the internet:

$$mathcal{B}_1$$ is the Sorgenfrey line. What I did not know is that $$b$$ doesn’t need to be real in order to get the line topology. How can i show this?
I have found that $$mathcal{B}_2$$ is also a Topology (on $$mathbb{R}$$?) but is not equivalent with the Sorgenfrey line. I cannot find anywhere proofs for this and I don’t have an idea how to show this.
In general: Is there somewhere an overview for all the topologies on $$mathbb{R}$$ generated by all the intervals?