Is a Bounded Set in R Countable if it Can be Covered by an Epsilon Cover?

[sayan2009]

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)

 

[Dick]

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.

 

[sayan2009]

oooooooooooo gr888888888...thanks