Abstract. In this paper we study the set of functions G-valued which can be approximated by G-valued continuous functions in the norm L∞G (I, w), where I is a compact interval, G is a real and separable Hilbert space and w is certain G-valued weakly measurable weight. Thus, we obtain a new extension of celebrated Weierstrass approximation theorem. Also, we characterize the set of functions whic...

Abstract Given a commutative semiring with compatible preorder satisfying version of the Archimedean property, asymptotic spectrum, as introduced by Strassen (J. reine angew. Math. 1988), is an essentially unique compact Hausdorff space together map from to ring continuous functions. Strassen’s theorem characterizes relaxation that asymptotically compares large powers elements up subexponential...

Pseudorandom encoding with quantized real modulation values encodes only continuous real-valued functions. However, an arbitrary complex value can be represented if the desired value is first mapped to the closest real value realized by use of pseudorandom encoding. Examples of encoding real- and complex-valued functions illustrate performance improvements over conventional minimum distance map...

A widely used theorem of analysis asserts that a uniformly bounded, equicontinuous family of functions has a compact closure in the space of continuous functions. This lemma, variously attributed to Arzela, Escoli, Montel, Vitali, and so on, is of importance in the theory of integral equations, conformal mapping, calculus of variations, and so on. In recent years the lemma has been generalized ...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

For a zero-dimensional topological space X and totally ordered field F with interval topology, Cc(X, F) denotes the ring consisting of field-valued continuous functions countable range on X. This article aims to study investigate rings quotients Cc(X,F). Qc(X,F) (resp. qc(X,F)), maximal classical) Cc(X,F) as modified analogue Q(X) q(X)), C(X) are characterized. It is proved that Qc(S), subring ...