Computing Simple Circuits from a Set of Line Segments.
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.
In this paper, we establish two constant selection theorems for a map whose dual is upper or lower semicontinuous. As applications, matching theorems, analytic alternatives, and minimax inequalities are obtained.