On the complexity of some $\sigma$-ideals of $\sigma$-P-porous sets
Zajíček, Luděk ; Zelený, Miroslav
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003), p. 531-554 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2003-01-01
Classification:  28A05,  54H05,  54H25 
@article{119407,
     author = {Lud\v ek Zaj\'\i \v cek and Miroslav Zelen\'y},
     title = {On the complexity of some $\sigma$-ideals of $\sigma$-P-porous sets},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {44},
     year = {2003},
     pages = {531-554},
     zbl = {1099.54029},
     mrnumber = {2025819},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119407}
}

Zajíček, Luděk; Zelený, Miroslav. On the complexity of some $\sigma$-ideals of $\sigma$-P-porous sets. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 531-554. http://gdmltest.u-ga.fr/item/119407/

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