Date: Feb 1, 2013 11:37 AM
Author: Achimota
Subject: looking for example of closed set that is *not* complete in a metric space
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.

Many thanks in advance,

Dan