Suppose that A is a subset of X and B is a subset of Y a Pro

Suppose that A is a subset of X and B is a subset of Y.
(a) Provide an example demonstrating that boundary(A x B) = boundary(A) x boundary(B) does
not hold in general.
(b) Derive and prove a relationship expressing boundary(A x B) in terms of boundary(A),
boundary(B), A, and B.

Solution

In reply to \"Suppose that A subset of X and B subset of Y\", posted by jack on October 15, 2013:
>Suppose that A subset of X and B subset of Y.
>(a) Provide an example demonstrating that boundary(A x B) = boundary(A) x boundary(B) does
>not hold in general.

Take A = B = [0,1] subset R = X = Y, usual topology.