On optimality of the index of sum, product, maximum, and minimum of finite Baire index functions

Authors

  • A. Zulijanto Department of Mathematics, Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia Author

Keywords:

Finite Baire index, oscillation index, Baire-1 functions

Subjects:

26A21, 54C30, 03E15

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)i(f)+i(g), where h is any of the functions f+g, fg, fg, fg. In this paper, we prove that the result is optimal in the following sense : for each n,k<ω,there exist functions f,g such that i(f)=n, i(g)=k, and i(h)=i(f)+i(g).

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Published

2017-07-15