- #1
gottfried
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Homework Statement
Find the error in this proof and give an example in (ℝ,de) to illustrate where this proof breaks down.
Proof that every totally bounded set in a metric space is bounded.
The set S is totally bounded and can therefore be covered by finitely many balls of radius 1, say N balls of radius 1. Then S is a subset of any ball B(x,2N) provided X lies in S. Thus diam S≤4N so that S is bounded.
I can't see the fault in the proof and therefore don't know where to start when looking for an example in (ℝ,de) that illustrates how the proof breaks down.
Any suggestions?