f(x) is said to be continuous when lim(x->a+)f(x)=lim(x->a-)f(X)=f(a).

where a is any point in the domain.

following a similar analogy for your 2 variable function i think f(x,y)is continuous everywhere as f(a,a)=0=lim(x->a+-)lim(y->a+-)f(x,y) in the domain which means that all the points of continuity will lie in the

domain. and the domain is given by whenever x>y for all reals.