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.
Publié le : 2002-05-14
Classification:
continuous restictions,
Borel functions,
descriptive set theory,
Hausdorff metric,
26A15,
03E75,
54A25
@article{1150118734,
author = {Jordan, Francis},
title = {Ideals of compact sets associated with Borel functions.},
journal = {Real Anal. Exchange},
volume = {28},
number = {1},
year = {2002},
pages = { 15-31},
language = {en},
url = {http://dml.mathdoc.fr/item/1150118734}
}
Jordan, Francis. Ideals of compact sets associated with Borel functions.. Real Anal. Exchange, Tome 28 (2002) no. 1, pp. 15-31. http://gdmltest.u-ga.fr/item/1150118734/