CONCERNING EQUIVALENCIES OF ALMOST CONTINUOUS AND CONNECTIVITY FUI~CTIONS

whenever a function of Baire class 1, f: I + I, has the Darboux property, then that function is a connected subset of the plane. For real functions with domain a connected sUbset of the real line, the property of a function being a connected subset of the plane, and the property of a function being a connectivity function are the same. Stating the Kuratowski-Sierpinski result in this terminology we have: a necessary and sufficient condition that the Baire class 1 function f: I + I, be a Darboux function is that it be a con nectivity function. Intuitively, when considering various generalizations of continuity, there are three classes of discontinuous functions which seem to be inherently compara ble or interrelated: Darboux functions, connectivity func tions, and almost continuous functions. Thus there was the obvious question of whether or not the Kuratowski-Sierpinsk