This is not directly a homework problem, so I opted not to place this question there. From what I have read/gathered from the internet/my textbook, a quotient mapping is any surjective, continuous mapping from a space X to a space comprised of the equivalence classes of all x in X from a relation ~. Is there anything more to it? I could find no one source that spelled out the definition for me, complete with all the conditions that must be satisfied to constitute one. The question that prompted this was something to the effect of proving a particular mapping from an arbitrary space to a subset of that space was a quotient map, and I was given the information indirectly that it was an onto mapping that was continuous. I basically made up an equivalence relation that satisfied the definition of the particular mapping, and that seemed like enough.