All the recursive real functions are continuous; in fact all the B-recursive real functions are continuous for any oracle B, simply because Turing Machines computing them are nite objects. But simple functions like step functions have to be in some sense be \easy" if they have recursive values and break points, although by our usual deeni-tion, they are not computable at all. So it seems unfair...

A fundamental aspect of harmonic analysis on Euclidean spaces deals with various classes of real or complex-valued functions, such as the C classes of functions which are continuous and continuously differentiable up to order k, where k is a nonnegative integer. If k = 0, this simply means that the function is continuous. Of course continuity of a function makes sense on any metric space, or on...

In point set topology—or, more precisely, in the part of it once called "theory of abstract spaces"—there are two principal methods of investigation. The first one refers to the topological space alone(2) ; we shall call it the internal method : for example the separation axioms Po, Pi, T2 [A-H], the notions of regularity, normality, compactness, are expressed in terms of the topological space ...

in this paper we study the relationships existing between total measurability in variation and gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. we also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regula...

In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain , has been introduced and several results, similar to well-known results constrained in terms approximants, have established. Further, some clue construction using concept fractal interpolation added. last part, multi-valued operators associated with $$...