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Concerning sets of the first Baire category with respect to different metrics

Moszyńska M., Sójka G.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 1

47-54

We prove that if ρH and δ are the Hausdorff metric and the radial metric on the space Sn of star bodies in R, with 0 in the kernel and with radial function positive and continuous, then a family A ⊂ Sn that is meager with respect to ρH 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 Sn with respect to δ.