Thank you for your help.
To tell the truth I don't know how to continue, how to use that in the problem.
He's saying that if you consider giving the usual topology induced by the usual norm then the induced topology is the same as if the product topology (when both copies of the reals are endowed with the usual topology). That said, for the product topology it's easy to prove things like . So now since are both dense in you can conclude that is dense in . etc.