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2004-2005 The Equality Between Borel and Baire Classes
H. R. Shatery, J. Zafarani
Real Anal. Exchange 30(1): 373-384 (2004-2005).


In this paper, we study some properties of the Banach space $\beta_{\alpha}(X)$, which consists of all real Baire functions on a perfectly normal space $X$. We obtain the equality between Baire and Borel classes as a consequence of existence of an approximation property and a Tietze extension for these classes. Moreover, when $Y$ is a zero dimensional topological space, we obtain a refinement of the known results for the equality between ${\beta}_{\alpha}^{\circ}(X,Y)$ and $B_{\alpha}^{\circ}(X,Y)$.


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H. R. Shatery. J. Zafarani. "The Equality Between Borel and Baire Classes." Real Anal. Exchange 30 (1) 373 - 384, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 27 July 2005

zbMATH: 1074.26003
MathSciNet: MR2127543

Primary: 26A21
Secondary: 54C20 , 54D15

Keywords: Baire functions , Borel functions , Tietze extension , Zero dimensional spaces

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 1 • 2004-2005
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