Let E be a proper subset of R. There is a point p not in E s.t for any e>0, there exists a point q in E s.t |p-q|<e. Prove that E is not compact.(adsbygoogle = window.adsbygoogle || []).push({});

Proof:

p is in R-E. For a e>0, p+e is in E. So R-E is closed on one side which implies E is open on one side. By using heine-borel thrm we can conclude that E is not compact.

Is this proof valid?

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# There is a point p not in E s.t for any e>0

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