I want to prove that the only continuous function from $R$ (with usual topology) to $R$ ( the Sorgenfrey line's $R_l$ Lower limit topology) is constant function.
My attempt is using the the properties of connected space. BOWC, assume there is continuous function which are not constant and surjective Since $f(R)$ is connected with more than one points. Then, it must be interval and $f(R)$ as subspace of $R_l$. I can not complete. I am asking wether or not my solution right.