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Maximal classes for lower and upper semicontinuous strong Świątkowski functions

Szczuka P.

Demonstratio Mathematica

2014

Vol. 47, nr 1

48--55

In this paper, we characterize the maximal additive and multiplicative classes for lower and upper semicontinuous strong Świątkowski functions and lower and upper semicontinuous extra strong Świątkowski functions. Moreover, we characterize the maximal class with respect to maximums for lower semicontinuous strong Świątkowski functions and lower and upper semicontinuous extra strong Świątkowski functions.

On the sets of continuity points of Darboux quasicontinuous functions

Grande M.

Demonstratio Mathematica

2003

Vol. 36, nr 4

819--825

We show that for every dense G-set A C R there is a Baire 1 Darboux bilaterally quasicontinuous function f : R-R such that C(f) = A, where C(f) denotes the set of all continuity points of f. Moreover we prove that for each G-set A there is a Baire 2 Darboux function f : R-R such that C(f) = A.