Let $\mathbb{R}_{\ell}$ the Sorgenfrey line and let $\mathbb{Q}$ endowed with usual topology.
I have two questions:
1) Is there a continuous surjective map $f: \mathbb{R}_{\ell} \rightarrow \mathbb{Q}$?
2) Is there a continuous surjective map $f: \mathbb{R}_{\ell} \rightarrow \mathbb{R}$ where $\mathbb{R}$ has the usual topology?
Not sure where to start. Can you please help?