Concerning Sets of the First Baire Category with Respectto Different Metrics

摘要

We prove that if QH and δ are the Hausdorff metric and the radial metric on the space S~n of star bodies in R~n, with 0 in the kernel and with radial function positive and continuous, then a family A < S~n that is meager with respect to QHneed not be meager with respect to δ. Further, we show that both the family of fractal star bodies and its complement are dense in S~n with respect to δ.