Let f, g,… be R-valued functions defined on a set X endowed with a topology (In many instances X is, for some n, a subset of R“.) The following facts about R and functions f, g,… are the basis of much of the subsequent discussion. The set of points of continuity resp. discontinuity of a function f is denoted Cont(f) resp. Discont(f). If f E ’ the set of points where f’ exists (does not exist) is denoted Diff(f) (Nondiff(f))
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