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Determination of convex bodies by infinity-chord functions

100%

Sójka G.

Demonstratio Mathematica

2010

tom Vol. 43, nr 1

187-202

In 1998 A. Soranzo introduced the notions of +infinity - and - infinity-chord functions (see [16]). In this paper we give an answer to the question when a convex body is determined by the values of -infinity-chord functions at chosen internal points. We also give some partial results regarding + infinity chord functions.

Some results about +nieskończoność-, -nieskończoność- and i-chord functions

63%

Soranzo A. , Sójka G.

Demonstratio Mathematica

2006

tom Vol. 39, nr 1

183-194

This paper concerns determination of a convex bodies by values of +oo- -oo-and i-chord functions. We prove that any at least two-dimensional convex body is not determined by values of -oo-chord functions at any two internal points. We also present some positive results on determination of convex bodies using -oo- or +oo-chord function at one point and i-chord function at other one.

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

63%

Moszyńska M. , Sójka G.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

tom 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.