Let A = R^2 - {(0,0)} and B = {(x,y); abs y < x^2}. Define filterbases A = {A intersection B_e(0,0): e>0} and B = {B intersection B_e(0,0): e>0}. Defind f on A by f(x,y) = (x^2-y^2)/(x^2 + y^2). Prove that the limit of f along A does not exist, but the limit of f along B does.
Thanks.