Geodesic
On the complexity of some $\sigma$-ideals of $\sigma$-P-porous sets
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 3, pp. 531-554.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $\bold P$ be a porosity-like relation on a separable locally compact metric space $E$. We show that the $\sigma$-ideal of compact $\sigma$-$\bold P$-porous subsets of $E$ (under some general conditions on $\bold P$ and $E$) forms a $\boldsymbol \Pi_{\bold 1}^{\bold 1}$-complete set in the hyperspace of all compact subsets of $E$, in particular it is coanalytic and non-Borel. Our general results are applicable to most interesting types of porosity. It is shown in the cases of the $\sigma$-ideals of $\sigma$-porous sets, $\sigma$-$\langle g \rangle$-porous sets, $\sigma$-strongly porous sets, $\sigma$-symmetrically porous sets and $\sigma$-strongly symmetrically porous sets. We prove a similar result also for $\sigma$-very porous sets assuming that each singleton of $E$ is very porous set.
Classification : 28A05, 54H05, 54H25
Keywords: $\sigma $-porous sets; $\sigma $-ideal; coanalytic sets; Hausdorff metric 
@article{CMUC_2003__44_3_a11,
     author = {Zaj{\'\i}\v{c}ek, Lud\v{e}k and Zelen\'y, Miroslav},
     title = {On the complexity of some $\sigma$-ideals of $\sigma${-P-porous} sets},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {531--554},
     publisher = {mathdoc},
     volume = {44},
     number = {3},
     year = {2003},
     mrnumber = {2025819},
     zbl = {1099.54029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2003__44_3_a11/}
}
TY  - JOUR
AU  - Zajíček, Luděk
AU  - Zelený, Miroslav
TI  - On the complexity of some $\sigma$-ideals of $\sigma$-P-porous sets
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2003
SP  - 531
EP  - 554
VL  - 44
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2003__44_3_a11/
LA  - en
ID  - CMUC_2003__44_3_a11
ER  - 
%0 Journal Article
%A Zajíček, Luděk
%A Zelený, Miroslav
%T On the complexity of some $\sigma$-ideals of $\sigma$-P-porous sets
%J Commentationes Mathematicae Universitatis Carolinae
%D 2003
%P 531-554
%V 44
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2003__44_3_a11/
%G en
%F CMUC_2003__44_3_a11
Zajíček, Luděk; Zelený, Miroslav. On the complexity of some $\sigma$-ideals of $\sigma$-P-porous sets. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 3, pp. 531-554. http://geodesic.mathdoc.fr/item/CMUC_2003__44_3_a11/