Re: What is the relation between Cauchy sequence and convergent sequence?

In article <1130875683.538294.27700@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
lucy <losemind@xxxxxxxxx> wrote:

>"Depends on your definition of "trivial". Take as a metric space the
>subspace of R given by [0,1] U [2,3] with the usual induced
>metric. Then both [0,1] and [2,3] are open in R, both nontrivial, and
>both complete. In this case, the two sets are clopen (both open and
>closed), of course, so maybe you want to throw those into your
>definition of "trivial.""
>
>->[0, 1] and [2, 3] are closed in R, right?

He meant to say "open in the metric space", not "open in R".

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.