>>11033980Could you first equally split I into k sub-intervals then use BCT on each sub-interval?
Let B(j) be the interval in the jth sub-interval and n(j) be element of N that is dense in B(j).
Let N(k) = sup{n(j)}.
f^(N(k)) is identically zero on each B(j).
The gap between B(j) and B(j+1) is less than 2/k.
Can the gaps somehow be filled in using smoothness?
Or can you just let k go to infinity and say the set that f^(N(k)) vanishes on becomes dense?
