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.

Kategorie tematyczne

• 54E52: Baire category, Baire spaces
• 28A80: Fractals
• 52A30: Variants of convex sets (star-shaped, ( m , n )-convex, etc.)

• 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