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

Maria Moszyńska, and Grzegorz Sójka. "Concerning Sets of the First Baire Category with Respect to Different Metrics." Bulletin of the Polish Academy of Sciences. Mathematics 58.1 (2010): 47-54. <http://eudml.org/doc/281228>.

@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 -