On the reduction of pairs of bounded closed convex sets

• Autorzy: J. Grzybowski , D. Pallaschke , R. Urbański
• Języki publikacji: EN

Abstrakty

EN

Let X be a Hausdorff topological vector space. For nonempty bounded closed convex sets A,B,C,D ⊂ X we denote by A ∔ B the closure of the algebraic sum A + B, and call the pairs (A,B) and (C,D) equivalent if A ∔ D = B ∔ C. We prove two main theorems on reduction of equivalent pairs. The first theorem implies that, in a finite-dimensional space, a pair of nonempty compact convex sets with a piecewise smooth boundary and parallel tangent spaces at some boundary points is not minimal. The second theorem generalizes and unifies two main techniques of reduction of pairs of compact convex sets.

Kategorie tematyczne

• 49J52: Nonsmooth analysis
• 26A51: Convexity, generalizations
• 52A07: Convex sets in topological vector spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 189
• Numer: 1
• Strony: 1-12

Daty

wydano

2008

Twórcy

autor

J. Grzybowski

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, PL-61-614 Poznań, Poland

autor

D. Pallaschke

• Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Kaiserstr. 12, D-76128 Karlsruhe, Germany

autor

R. Urbański

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, PL-61-614 Poznań, Poland

Identyfikatory

DOI

10.4064/sm189-1-1