On the sums of unilaterally approximately continuous and approximate jump functions. (English) Zbl 1061.26004

In the earlier paper [Demonstr. Math. 35, No. 4, 743–748 (2002; Zbl 1036.26003)] the author has proved that every jump function is the sum of two unilaterally continuous jump functions. This paper contains the construction of an example showing that a similar result does not hold for the density topology in the place of the ordinary topology on the real line. However, Theorem 2 says that under an additional condition concerning the set where the approximate oscillation is greater or equal to a positive number the representation of an approximate jump function as a sum of two unilaterally approximately continuous functions and approximate jump functions is possible.


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


Zbl 1036.26003
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