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Concerning Sets of the First Baire Category with Respect to Different Metrics

Maria Moszyńska, Grzegorz Sójka (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove that if ϱ H 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 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 ⁿ with respect to δ.

Constant selections and minimax inequalities

Mircea Balaj (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

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