MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
On optimality of the index of sum, product, maximum, and minimum of finite Baire index functions
A. Zulijanto

Abstract

Chaatit, Mascioni, and Rosenthal defined finite Baire index for a bounded real-valued function $f$ on a separable metric space, denoted by $i(f)$, and proved that for any bounded functions $f$ and $g$ of finite Baire index, $i(h)\leq i(f)+i(g)$, where $h$ is any of the functions $f+g$, $fg$, $f\vee g$, $f\wedge g$. In this paper, we prove that the result is optimal in the following sense : for each $n,k<\omega$, there exist functions $f,g$ such that $i(f)=n$, $i(g)=k$, and $i(h)=i(f)+i(g)$.

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Keywords: Finite Baire index; oscillation index; Baire-1 functions.

MSC: 26A21, 54C30, 03E15

Pages:  207--213     

Volume  69 ,  Issue  3 ,  2017