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On some representations of functions discontinuous on countable sets

Błaszczyk T., Grande Z.

Demonstratio Mathematica

2001

Vol. 34, nr 3

543-548

It is proved that every function f : R -> R having countably many of discontinuity points is the sum of two bilaterally quasi-continuous functions which are continuous at every continuity point of f.

Covering Baire 1 functions with darboux functions and the cofinality of the ideal of meager sets

Jordan F.

Journal of Applied Analysis

1999

Vol. 5, nr 1

71-94

Let Dar stand for the Darboux Baire class 1 functions. We show that the cofinality of the meager sets in R is the smallest cardinality of a set of Baire class 1 functions F such that for any finite collection of Baire class 1 functions G there is an f ∈ F such that f + G ⊆ Dar. Other results of this type are shown. These results are then considered as statements about additivity. The notion of super-additivity is introduced.