Consider f:RR where f(x)=x. Does f have a limit at 0 if we use dD for the domain and dE for the co-domain? How about if we use dE for the domain and dD for the co-domain? Problem 4 Consider two metric spaces (X,dX) and (Y,dY). Show that if X is finite, then there does not exist a function f:XY that is continuous. Problem 5 Prove that given metric spaces (X,dX),(Y,dY),(Z,dZ), if f:XY is contiuous at x0 and g:YZ is continuous at f(x0), then the composite function gf:XZ is continuous at x0. Problem 6 Prove that the function f:RR where f(x)=x is continuous