A LINEARLY FIBERED SOUSLINEAN SPACE UNDER MA

Abstract. Under Martin’s Axiom a c.c.c. nonseparable compact space is constructed which maps continuously into [0, 1] with linear fibers. Such a space can not, for instance, map onto [0, 1]ℵ1. 1. Introduction. In 1920, Souslin asked whether the countable chain condition is a sufficient re-striction on linear compacta to imply that they are metrizable [6]. Although the answer was shown to be independent of ZFC in the 1960’s, this now classic ques-tion has led to a prominent theme of modern set theoretic topology: c.c.c. versu