Re: Open balls

Let (M,d) be a metric space. Denote with B(p,t) the
open ball with center p
and radius t.
If B(x,r) <= B(x,s) then it is not necessarily r<=s.
I'm a little rusty in this area, but could you show a proof of this?

What happens if B(x,r) < B(x,s) (that is, B(x,r) is
strictly included in
B(x,s) ) ? Can we say once again that it is not
necessarily r<=s ?


I suspect that if you can prove the statement I question, you can prove this also.
.

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