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 $i\left(f\right)$, and proved that for any bounded functions $f$ and $g$ of finite Baire index, $i\left(h\right)\le i\left(f\right)+i\left(g\right)$, 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 $i\left(f\right)=n$, $i\left(g\right)=k$, and $i\left(h\right)=i\left(f\right)+i\left(g\right)$.

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

Classification (MSC2000): 26A21; 54C30, 03E15

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