```Date: Feb 1, 2013 5:16 PM
Author: Butch Malahide
Subject: Re: looking for example of closed set that is *not* complete in a<br> metric space

On Feb 1, 10:37 am, "Daniel J. Greenhoe" <dgreen...@yahoo.com> wrote:> 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? I don't know for sure that it is not true, but I might> guess that it is not true.Do you happen to know an example of a metric space which is notcomplete? If so, let (X,d) be that metric space, and let Y = X.If not, do you know an example of a metric space in which some subsetis not closed? In that case, let (W,d) be that metric space, let X bea non-closed subset of W, and let Y = X. Then (X,d) is an incompletemetric space, (Y,d) is a closed subspace of (X,d), and (Y,d) is notcomplete.
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