Continuous functions in rings generated by a single Darboux function

Paweł Barbarski

doi:10.14321/realanalexch.46.1.0083

Abstract

The problem of characterizing continuous functions belonging to each $\mathcal A$-ring containing a fixed Darboux function is fully solved for a compact interval domain and solved with some minor exception for a real line domain. Many properties of generated $\mathcal A$-rings and their continuous functions are stated.

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Paweł Barbarski. "Continuous functions in rings generated by a single Darboux function." Real Anal. Exchange 46 (1) 83 - 98, 2021. https://doi.org/10.14321/realanalexch.46.1.0083

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Published: 2021

First available in Project Euclid: 14 October 2021

Digital Object Identifier: 10.14321/realanalexch.46.1.0083

Subjects:

Primary: 26A15

Secondary: 26A12 , 46E25 , 46J10

Keywords: Continuous function , Darboux function , family of functions separating elements of a partition , polynomially bounded function , ring generated by a function , ring of functions , Stone-Weierstrass theorem

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