Prove that any countable subset of R has empty interior. Is the converse true?

this is one of the question in my midterm that i couldnt do, the prof are not giving out solution, need some help to prove this

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- December 3rd 2011, 06:52 PMwopashuiprove subset of R has empty interior
Prove that any countable subset of R has empty interior. Is the converse true?

this is one of the question in my midterm that i couldnt do, the prof are not giving out solution, need some help to prove this - December 3rd 2011, 07:23 PMDrexel28Re: prove subset of R has empty interior
- December 4th 2011, 07:37 PMwopashuiRe: prove subset of R has empty interior
cardinality of (a,b) is continunm, so this implies that X is uncontable, which is a contridiction?

- December 4th 2011, 07:43 PMDrexel28Re: prove subset of R has empty interior
- December 6th 2011, 03:15 PMwopashuiRe: prove subset of R has empty interior
what could be an explicit counter example for the converse?

that is we need to find a subset C of R such that int(C)=empty but C is uncountable - December 11th 2011, 11:20 PMDrexel28Re: prove subset of R has empty interior