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

Grande, Marcin

Real Anal. Exch. 28(2002-2003), No. 2, 623-630 (2003).

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.

Reviewer: Jerzy Niewiarowski (Łódź)

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

Keywords:

approximate limits; approximate continuity

Citations:

Zbl 1036.26003