Re: balls and metric

On Sat, 29 Apr 2006, William Elliot wrote:
On Sat, 29 Apr 2006, [ISO-8859-1] José Carlos Santos wrote:
On 29-04-2006 17:00, A N Niel wrote:

Give an example of a metric space in which a ball of
radius 4 is contained in a ball of raduis 3.
Any metric space with a single point.

Now do one strictly contained in...
That was not required. :-)

S = { 0,1,2,3,4 }; d(n,m) = |n - m|
B(4,4) = { 1,2,3,4 } proper subset S = B(2,3)

S = [0,4]
B(4,4) = (0,4] proper subset [0,4] = B(2,3)

S = (-5,5) or S = (-oo,5)
B(4,4) = (0,5) proper subset (-1,5) = B(2,3)
.

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