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looking for example of closed set that is *not* complete in a metric space
Posted:
Feb 1, 2013 11:37 AM
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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
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