Hi
Let A and B be two closed and bounded sets in a complete metric space
X. Suppose
d(A, B) = inf {d(a, b) : a in A, b in B} = 0. Does it necessarily mean
that A and B intersect?
Thanks.

Quote:
Hi
Let A and B be two closed and bounded sets in a complete metric space
X. Suppose
d(A, B) = inf {d(a, b) : a in A, b in B} = 0. Does it necessarily mean
that A and B intersect?
Thanks.


Hint: In l^2, which is complete, A = {e_n : n in N} is a closed
bounded set, and you can modify A a bit to arrive at an
interesting candidate for B.

zee  

--Last edited by zee on 2007-01-27 04:49:15 --