Colouring and non-productivity of ℵ2-C.C. Original Research Article

We prove that colouring of pairs from with strong properties exists. The easiest to state (and quite a well-known) problem it solves is: there are two topological spaces with cellularity whose product has cellularity ; equivalently, we can speak of cellularity of Boolean algebras or of Boolean algebras satisfying the whose product fails the We also deal more with guessing of clubs.