A Note on Cauchy-type Class of Functions Made Tantrawan, Hadrian Andradi, Atok Zulijanto, Dewi Kartika Sari
Universitas Gadjah Mada
Abstract
Continuous and Baire-1 functions are two important types of functions in mathematics and applied science. They often play a crucial role in comprehending and modeling natural phenomena and making better decisions in various situations. In mathematical term, continuous functions are defined through the -\epsilon-\delta- formulation, while Baire-1 functions are defined as limits of sequences of continuous functions. Since 2001, it has been known that Baire-1 functions can also be formulated in terms of -\epsilon-\delta-. Based on this fact, a natural question arises about classes of functions between continuous and Baire-1 functions that can also be characterized in terms of -\epsilon-\delta-. Some answers have been obtained by Jachymski and Lindner (2004), but with certain assumptions. In this paper, we generalize some of the results on characterization of those classes of functions. We also provide alternative proofs of several cases of when the class is equal to the class of continuous functions or Baire-1 functions.
Keywords: Baire-1 functions, continuous functions, Cauchy-type function
