On the Countable Tightness of Product Spaces

In this paper, we discuss the countable tightness of products of spaces which are quotient simages of locally separable metric spaces, or kspaces with a starcountable knetwork. The main result is that the following conditions are equivalent: (1) b = 1; (2) t(S S 1 ) > ; (3) For any pair (X, Y ), which are kspaces with a pointcountable knetwork consisting of cosmic subspaces, t(X Y ) if and only if one of X, Y is first countable or both X, Y are locally cosmic spaces. Many results on the kspace property of products of spaces with certain knetworks could be deduced from the above theorem.