OPENNESS POINTS OF THE PROJECTION MAP OF CONVEX BODIES OF CONSTANT WIDTH

Анотація

It is proved that the set of points at which the projection map of the hyperspace of compact convex bodies of constant width in ${\mathrm{ℝ}}^3$ onto the corresponding hyperspace in ${\mathrm{ℝ}}^2$ is not open, is dense in the hyperspace. A similar result can be proven for the projection of ${\mathrm{ℝ}}^n$ onto ${\mathrm{ℝ}}^2$, where $n>2$.