Prove that the following statements are equivalent

Hi

I'm trying to prove that the following two staments are equivalent.

Let A and B be closed subsets of Rd, and suppose that A is bounded.

i) A and B are disjoint

ii) There exists a pair of sequences (xn) (subset of A) and (yn) (subset of B) such that

lxn-Ynl->0.

Any help would be appreciated, not too sure here to start.

Re: Prove that the following statements are equivalent

Quote:

Originally Posted by

**icedtea** I'm trying to prove that the following two staments are equivalent.

Let A and B be closed subsets of Rd, and suppose that A is bounded. i) A and B are disjoint

ii) There exists a pair of sequences (xn) (subset of A) and (yn) (subset of B) such that

lxn-Ynl->0.

Any help would be appreciated, not too sure here to start.

What is

Re: Prove that the following statements are equivalent

Sorry. Thats my fault, kind of new to this.

Rd should be the set of reals with dimension d.

Re: Prove that the following statements are equivalent

Re: Prove that the following statements are equivalent

What if the sets A and B were unbounded? Would the statements hold?

Re: Prove that the following statements are equivalent

Quote:

Originally Posted by

**icedtea** What if the sets A and B were unbounded? Would the statements hold?

Let they are unbounded, disjoint, closed sets. If then .

Now answer your own question?

Re: Prove that the following statements are equivalent