Characters of ultrafilters and tightness of products of fans

As applications of productivity of coreflective classes of topological spaces, the following results will be proved: (1) Characters of points of βN?N are not smaller than any submeasurable cardinal less or equal to ω². (2) If κ is a submeasurable cardinal and S is a sequential fan with κ many spines then the tightness of the κ-power of S is equal to κ. In fact, a little more general results are proved.