Concerning Sets of the First Baire Category
with Respect to Different Metrics
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 1, pp. 47-54
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We prove that if $\varrho_H$ and $\delta$ are the Hausdorff metric and the radial metric on the space $\mathcal{S}^n$ of star bodies in
$\mathbb R $, with 0 in the kernel and with radial function positive and continuous, then a family $\mathcal{A} \subset \mathcal{S}^n$ that is meager with respect to $\varrho_H$ need not be meager with respect to $\delta$. Further, we show that both the family of fractal star bodies and its complement
are dense in $\mathcal{S}^n$ with respect to $\delta$.
Keywords:
prove varrho delta hausdorff metric radial metric space mathcal star bodies mathbb kernel radial function positive continuous family mathcal subset mathcal meager respect varrho meager respect delta further family fractal star bodies its complement dense mathcal respect delta
Affiliations des auteurs :
Maria Moszyńska 1 ; Grzegorz Sójka 2
@article{10_4064_ba58_1_6,
author = {Maria Moszy\'nska and Grzegorz S\'ojka},
title = {Concerning {Sets} of the {First} {Baire} {Category}
with {Respect} to {Different} {Metrics}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {47--54},
year = {2010},
volume = {58},
number = {1},
doi = {10.4064/ba58-1-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba58-1-6/}
}
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%0 Journal Article %A Maria Moszyńska %A Grzegorz Sójka %T Concerning Sets of the First Baire Category with Respect to Different Metrics %J Bulletin of the Polish Academy of Sciences. Mathematics %D 2010 %P 47-54 %V 58 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/ba58-1-6/ %R 10.4064/ba58-1-6 %G en %F 10_4064_ba58_1_6
Maria Moszyńska; Grzegorz Sójka. Concerning Sets of the First Baire Category with Respect to Different Metrics. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 1, pp. 47-54. doi: 10.4064/ba58-1-6
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