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Mathematical Analysis Fundamentals by Agamirza Bashirov

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Chapter 6

Space C(E,E′)

Abstract

Chapter 6 contains a further discussion of continuous functions. The spaces of continuous functions as well as bounded functions are defined as metric spaces. The concepts of uniform continuity and uniform convergence are widely discussed. The completeness issue of the space of continuous functions is handled. Approximation of continuous functions by polynomials and some other kinds of functions in the form of Bernstein, Stone and Weierstrass theorems is considered. The chapter ends with the Ascoli-Arzelà theorem on compactness in the space of continuous functions.

Keywords

Uniform continuity; uniform convergence; approximation; equicontinuity

The structures of an atom and the solar system are very similar while ...

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