Answer to Question #130246 in Real Analysis for Brendan Zhang

Question

I need help with part 2 of the following question. Please show A separates points and rule out the set C_x0,y0. By Stone's theorem, this would imply uniform density. There's another poster on this site who gave a nonsense answer to this question.

Let X, Y be compact metric spaces. Let A = {(x, y) →summation i=1 to n fi(x)gi(y) | fi ∈ C(X, R), and gi ∈ C(Y, R), 1 ≤ i ≤ n}.

i. Show that A is an algebra.

ii. Show that A is uniformly dense in C(X × Y, R).

Answer 1

Dear Brendan Zhang, your question requires a lot of work, which neither of our experts is ready to perform for free. We advise you to convert it to a fully qualified order and we will try to help you. Please click the link below to proceed: Submit order