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1
Content available On ∞-entropy points in real analysis
EN
We will consider ∞-entropy points in the context of the possibilities of approximation mappings by the functions having ∞-entropy points and belonging to essential (from the point of view of real analysis theory) classes of functions: almost continuous, Darboux Baire one and approximately continuous functions.
2
Content available remote Maximal classes for lower and upper semicontinuous strong Świątkowski functions
EN
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.
3
Content available remote Maximums of upper semicontinuous strong Świątkowski functions
EN
In this paper we characterize the family of the maximums of upper semicontinuous strong Świątkowski functions and we show that the family of all upper semicontinuous strong Świątkowski functions is not closed with respect to maximums.
EN
The main goal of this paper is to characterize both the quotients of quasi-continuous and the quotients of Darboux quasi-continuous functions. We prove also theorems concerning common divisor for the families of the quotients of quasi-continuous (Darboux quasi-continuous) functions with respect to quasi-continuity (Darboux property and quasi-continuity, respectively).
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