Just curious how to define continuity for mult dim. functions. I know that the topological and set theorectical definitions work in a very abstract setting; but I just don't know how to prove (for example) that f(x,y) = x + y or f(t,z) = t*z is continuous, other than saying something like: Well because f(t)=t is continuous and ...., therefore the composition of.... and hence it is continuous. I was wondering if there is a generalization for delta-epsilon defition that would cover any (actual) function (as opposed to some abstract space,etc): R to R and R^n to R^m (where m,n are any positive integers and may or may not be equal). Can we possibly express epsilon-delta as a vector? A stretch maybe? Thanks for any help,.... I'm teaching myself topology and more analysis right now! got to love it!