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

In article <dk8j1a$5to$1@xxxxxxxxxxxxxxxxxxxxxx>,
Robert Israel <israel@xxxxxxxxxxx> wrote:
>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".

Oops. Quite right. Thank you for the correction.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

Relevant Pages

  • Re: "It is easy to see...."
    ... all this stuff cold, but it's been too many years... ... what I accept as reality." ... Arturo Magidin ... Prev by Date: ...
    (sci.math)
  • Re: Set of irrationals closed under sum
    ... and let A be the Z-span of S. ... what I accept as reality." ... Arturo Magidin ... Prev by Date: ...
    (sci.math)
  • Re: Dedekind Domain
    ... Sorry I can't be more detailed; I'm away from the office, and plan to ... what I accept as reality." ... Arturo Magidin ... Prev by Date: ...
    (sci.math)
  • Re: Split or Irreducible
    ... If u is a root for f, ... what I accept as reality." ... Arturo Magidin ... Prev by Date: ...
    (sci.math)
  • Re: A few more GRE questions
    ... Hmmm... ... what I accept as reality." ... Arturo Magidin ... Prev by Date: ...
    (sci.math)