I had mailed a professor in a certain department inquiring about graduate student openings and he replied saying that he lacks funding to hire anymore students. The same department has atleast two other professors who work in almost exactly the same domain albeit different numerical technique. My professor had advised me against mailing different professors from the same department, so should I request no objection from the prof who replied before mailing another one or can I go and mail them.
i Don’t understand the reason for the original admonishment, except if it’s based on the assumption that the professors might talk and thus decide to reject you from both groups. However, even given that, since the first professor has already said he can’t take on new students, there isn’t any reason you can’t still contact the others. You don’t need to ask the professor if there are no objections: the professor’s already done that by turning you down outright. The worst that can happen is that they will say no.