MATEMATIČKI VESNIK Vol. 69, No. 3, pp. 207–213 (2017) 

On optimality of the index of sum, product, maximum, and minimum of finite Baire index functionsA. ZulijantoDepartment of Mathematics, Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia Email: atokzulijanto@ugm.ac.idAbstract: Chaatit, Mascioni, and Rosenthal defined finite Baire index for a bounded realvalued 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; Baire1 functions. Classification (MSC2000): 26A21; 54C30, 03E15 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 20 Jun 2017. This page was last modified: 7 Jul 2017.
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