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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.
We prove that a C1,1-smooth bounded domain D in Cn is linearly convex if and only if the convex hull of any two discs in D with common center lies in D.
