On the sums of unilaterally approximately continuous and approximate jump functions. (Q595913)

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.