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Consistent recovery and polygonal approximation of functions. (English) Zbl 1050.26003

Authors’ abstract: “We consider real-valued functions defined on the unit interval. It is known that the class of first-return recoverable functions is the same as the class of polygonally approximable functions and that this class consists of the Baire one functions. Here we introduce the more restrictive classes of consistently first-return recoverable functions and consistently polygonally approximable functions. We show that these classes are identical and consist of those functions which are continuous except at countably many points.”

MSC:

26A21 Classification of real functions; Baire classification of sets and functions
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
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