In this article we are interested in the following problem: to find a map that satisfieswhere is an open set of and is a compact isotropic set of . We will show an existence theorem under suitable hypotheses on .
In this article we are interested in the following problem: to find a map that satisfies where Ω is an open set of and E is a compact isotropic set of . We will show an existence theorem under suitable hypotheses on φ.
We prove that if and δ are the Hausdorff metric and the radial metric on the space ⁿ of star bodies in ℝ, with 0 in the kernel and with radial function positive and continuous, then a family ⊂ ⁿ that is meager with respect to 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 ⁿ with respect to δ.
G. Beer defined the visibility function of a set S and proved its continuity in the interior of S. It is proved here that the visibility function of a planar Jordan domain is continuous precisely at the cone points of the boundary of S.