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On discrete limits of sequences of bilaterally quasicontinuous, Baire 1 functions. (English) Zbl 1009.26006

Summary: We show that for the discrete limit \(f\) of a sequence of bilaterally quasicontinuous Baire 1 functions the complement of the set of all points at which \(f\) is bilaterally quasicontinuous and has Darboux property, is nowhere dense. Moreover, a construction is given of a bilaterally quasicontinuous function which is the discrete limit of a sequence of Baire 1 functions, but is not the discrete limit of any sequence of bilaterally quasicontinuous Baire 1 functions.

MSC:

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