Problems(1)
A subset U⊂R is open if for any x∈U, there exist real numbers a,b such that x∈(a,b)⊂U. Suppose S⊂R has the property that any open set intersecting (0,1) also intersects S. Let T be a countable collection of open sets containing S. Prove that the intersection of all of the sets of T is not a countable subset of R.
(A set Γ is countable if there exists a bijective function f:Γ→Z.) combinatorics