×

zbMATH — the first resource for mathematics

Maximums of almost continuous functions. (English) Zbl 1107.26007
A classical result due to Sierpiński asserts that an arbitrary real-valued function defined on an interval can be written as the sum of two functions satisfying the intermediate value property (Darboux property). This result is extended in the present paper in the following sense: an arbitrary function \(f:\mathbb R\rightarrow\mathbb R\) can be written as the maximum of two almost continuous functions, provided \(f\) can be written as the maximum of two functions with the intermediate value property. The proof of this interesting results relies on elementary arguments in the theory of real functions.

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
54C08 Weak and generalized continuity
54C30 Real-valued functions in general topology
PDF BibTeX XML Cite
Full Text: DOI