Abstract
Unless otherwise specified, the sets with which we shall deal will be subsets of the open interval I= (0, 1). The term c-set will be used to describe a set each of whose points is a bilateral condensation point of the set. A d-set will be a set that has metric density 1 at each of its points. (Clearly, every d-set is a c-set, but not conversely.) In this terminology, a necessary and sufficient condition for a functionf to belong to the first Baire class and possess the Darboux (intermediate value) property is that for every real number a, the sets
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