Abstract
The Machado–Bishop theorem for weighted vector-valued functions vanishing at infinity has been extensively studied. In this paper, we give an analogue of Machado’s distance formula for bounded weighted vector-valued functions. A number of applications are given; in particular, some types of the Bishop–Stone–Weierstrass theorem for bounded vector-valued continuous spaces in the uniform topology are discussed; the splitting of C(I×J,X⊗Y) as the closure of C(I,X)⊗C(J,Y) in different senses and the extension of continuous vector-valued functions are studied.
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