
Re: closed but not complete
Posted:
Feb 2, 2013 12:27 AM


On Feb 1, 9:14 pm, William Elliot <ma...@panix.com> wrote: > On Fri, 1 Feb 2013, Daniel J. Greenhoe wrote: > > A long title in ignarance of what he once learned in composition class. > > > Let (Y,d) be a subspace of a metric space (X,d). > > > If (Y,d) is complete, then Y is closed with respect to d. That is, > > complete==>closed. > > > Alternatively, if (Y,d) is complete, then Y contains all its limit > > points. > > Would anyone happen to know of a counterexample for the converse? That > > is, does someone know of any example that demonstrates that > > closed > complete > > is *not* true? > > No. Assume K is a closed subset of the complete space (S,d).
But the original poster did not say that his metric space (X,d) was complete.

