Recław, Ireneusz Restrictions to continuous functions and Boolean algebras. (English) Zbl 0781.26003 Proc. Am. Math. Soc. 118, No. 3, 791-796 (1993). In this paper the author shows that every Borel function \(f: \mathbb{R}\to\mathbb{R}\) is continuous on a set \(A\not\in J\) if \(B(\mathbb{R})/J\) is weakly distributive (\(J\) is a proper ideal of a \(\sigma\)-algebra). Moreover, he investigates some other conditions concerning the problem of restrictions to continuous functions. Reviewer: R.Pawlak (Łódź) Cited in 3 Documents MSC: 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 28A10 Real- or complex-valued set functions 06E10 Chain conditions, complete algebras Keywords:weak distributivity; Borel function; \(\sigma\)-algebra; continuous functions PDFBibTeX XMLCite \textit{I. Recław}, Proc. Am. Math. Soc. 118, No. 3, 791--796 (1993; Zbl 0781.26003) Full Text: DOI