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Characterizations and properties of graphs of Baire functions

In: Mathematica Slovaca, vol. 68, no. 4
Balázs Maga

Details:

Year, pages: 2018, 789 - 802
Keywords:
Baire classes, graphs of functions, Fréchet spaces, Suslin spaces
About article:
Let $X$ be a paracompact topological space and $Y$ be a Banach space. In this paper, we will characterize the Baire-$1$ functions $f:X\rightarrow{Y}$ by their graph: namely, we will show that $f$ is a Baire-$1$ function if and only if its graph $\gr (f)$ is the intersection of a sequence $(Gn)n=1$ of open sets in $X×{Y}$ such that for all $x\in{X}$ and $n\in\mathbb{N}$ the vertical section of $Gn$ is a convex set, whose diameter tends to $0$ as $n\rightarrow∞$. Afterwards, we will discuss a similar question concerning functions of higher Baire classes and formulate some generalized results in slightly different settings: for example we require the domain to be a metrized Suslin space, while the codomain is a separable Fr
How to cite:
ISO 690:
Maga, B. 2018. Characterizations and properties of graphs of Baire functions. In Mathematica Slovaca, vol. 68, no.4, pp. 789-802. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0145

APA:
Maga, B. (2018). Characterizations and properties of graphs of Baire functions. Mathematica Slovaca, 68(4), 789-802. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0145
About edition:
Published: 10. 8. 2018