On biorthogonal systems whose functionals are finitely supported
We show that for each natural number n > 1, it is consistent that there is a compact Hausdorff totally disconnected space such that has no uncountable (semi)biorthogonal sequence where ’s are atomic measures with supports consisting of at most 2n-1 points of , but has biorthogonal systems where ’s are atomic measures with supports consisting of 2n points. This complements a result of Todorcevic which implies that it is consistent that such spaces do not exist: he proves that its is...