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

• Autorzy: Maria Moszyńska , Grzegorz Sójka
• Języki publikacji: EN

Abstrakty

EN

We prove that if $ϱ_H$ 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 $ϱ_H$ 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 𝓢ⁿ with respect to δ.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: 58
• Numer: 1
• Strony: 47-54

Daty

wydano

2010

Twórcy

autor

Maria Moszyńska

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

autor

Grzegorz Sójka

• Department of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-601 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba58-1-6