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2002-2003 Ideals of compact sets associated with Borel functions.
Francis Jordan
Author Affiliations +
Real Anal. Exchange 28(1): 15-31 (2002-2003).


We investigate the connection between the Borel class of a function $f$ and the Borel complexity of the set $\T(f)=\{C\in\comp(X)\colon f\rest_C\text{ is continuous}\}$ where $\comp(X)$ denotes the compact subsets of $X$ with the Hausdorff metric. For example, we show that for a function $f\colon X\to Y$ between Polish spaces; if $\T(f)$ is $F_{\sigma\delta}$ in $\comp(X)$, then $f$ is Borel class one.


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Francis Jordan. "Ideals of compact sets associated with Borel functions.." Real Anal. Exchange 28 (1) 15 - 31, 2002-2003.


Published: 2002-2003
First available in Project Euclid: 12 June 2006

zbMATH: 1053.54042
MathSciNet: MR1973965

Primary: 26A15
Secondary: 03E75 , 54A25

Keywords: Borel functions , continuous restictions , descriptive set theory , Hausdorff metric

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 1 • 2002-2003
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