The independence of certain distributive laws in Boolean algebras
Dana Scott · Transactions of the American Mathematical Society · 1957
LEMMA 1. There is a 0-dimensional Hausdorff space OC such that (i) the class of open sets of SC is closed under the formation of 13-termed intersections for every 13 <a; (ii) the class of nowhere-dense sets of 9 is closed under the formation of 13-termed unions for every 13 <a; (iii) there is an a X2-termed sequence C of nonempty open-closed sets of 9C such that (iii1) CtoUCti1= SXfor <a; and (iii2) n,. Ctf () is nowhere-dense for f E 2al.