SOUSLINS HYPOTHESIS AND CONVERGENCE IN CATEGORY

A sequence of functions f(n) : X --> R from a Baire space X to the rea ls R is said to converge in category iff every subsequence has a subse quence which converges on all but a meager set. We show that if there exists a Souslin tree, then there exists a nonatomic Baire space X suc h that every sequence which converges in category converges everywhere on a comeager set. This answers a question of Wagner and Wilczynski w ho proved the converse.