Concerning Sets of the First Baire Category with Respect to Different Metrics

@article{MariaMoszyńska2010,
abstract = {We prove that if $ϱ_H$ and δ are the Hausdorff metric and the radial metric on the space ⁿ of star bodies in ℝ, with 0 in the kernel and with radial function positive and continuous, then a family ⊂ ⁿ that is meager with respect to $ϱ_H$ need not be meager with respect to δ. Further, we show that both the family of fractal star bodies and its complement are dense in ⁿ with respect to δ.},
author = {Maria Moszyńska, Grzegorz Sójka},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {star body; radial metric; fractal star body},
language = {eng},
number = {1},
pages = {47-54},
title = {Concerning Sets of the First Baire Category with Respect to Different Metrics},
url = {http://eudml.org/doc/281228},
volume = {58},
year = {2010},
}

TY - JOUR
AU - Maria Moszyńska
AU - Grzegorz Sójka
TI - Concerning Sets of the First Baire Category with Respect to Different Metrics
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2010
VL - 58
IS - 1
SP - 47
EP - 54
AB - We prove that if $ϱ_H$ and δ are the Hausdorff metric and the radial metric on the space ⁿ of star bodies in ℝ, with 0 in the kernel and with radial function positive and continuous, then a family ⊂ ⁿ that is meager with respect to $ϱ_H$ need not be meager with respect to δ. Further, we show that both the family of fractal star bodies and its complement are dense in ⁿ with respect to δ.
LA - eng
KW - star body; radial metric; fractal star body
UR - http://eudml.org/doc/281228
ER -