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Compositions of Sierpiński-Zygmund functions from the left

Jordan F.

Journal of Applied Analysis

2001

Vol. 7, nr 1

81-89

A cardinal related to compositions of Sierpiński-Zygmund functions from the left, Cleft(SZ), will be considered. We answer a question of K. Ciesielski and T. Natkaniec. In particular, we show that cl(SZ) = (2c)+ if R is not a union of less than c-many meager sets and c is a limit cardinal. If c = ◛, then cl(SZ) is equal to the bounding number of c.

Compositions of Sierpiński-Zygmund functions and related combinatorial cardinals

Jordan F.

Journal of Applied Analysis

2001

Vol. 7, nr 2

243-255

A cardinal related to compositions of Sierpiński-Zygmund functions will be considered. A combinatorial characterization of the cardinal is given and is used to answer some questions of K. Ciesielski and T. Natkaniec. It is shown that the bounding number of the continuum may be strictly smaller than continuum.

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.