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Countable bounded set

  • Thread starter sayan2009
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  • #1
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Homework Statement



given a set A(subset of R(reals)) is bounded.and for all x belongs to R there exists epsilon(eps) such that {(x-eps,x+eps) intersection A} is countable..to prove A is countable

Homework Equations





The Attempt at a Solution

...bdd set in R is totally bounded...but iam not finding the way how to cover A by epsilon cover(has at most countable elements)
 

Answers and Replies

  • #2
Dick
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Take a closed interval C containing A and cover it with open intervals having a countable intersection with A. Now use the compactness of the closed interval C.
 
  • #3
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oooooooooooo gr888888888...thanks
 

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