Prove that the closure of a bounded set is bounded.

  • Thread starter dustbin
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  • #1
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Homework Statement



Prove that if S is a bounded subset of ℝ^n, then the closure of S is bounded.

Homework Equations



Definitions of bounded, closure, open balls, etc.

The Attempt at a Solution



See attached pdf.
 

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  • Problem.pdf
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Answers and Replies

  • #2
938
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That looks OK to me apart from a couple of typos.

There is an easier way to prove this too though. Do you know that the closure of S is the intersection of all closed subsets containing S?
 
  • #3
239
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Thanks for your input! We have not proved that the closure of S is the intersection of all closed subsets containing S... so I cannot use this result without proof.
 
  • #4
Dick
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Thanks for your input! We have not proved that the closure of S is the intersection of all closed subsets containing S... so I cannot use this result without proof.

Your original proof looks fine to me. Except when you pick an epsilon, it should be "there exists epsilon" not "for all epsilon".
 

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