Borsuk-Ulam type theorems

• Autorzy: Adam Idzik
• Języki publikacji: EN

Abstrakty

EN

A generalization of the theorem of Bajmóczy and Bárány which in turn is a common generalization of Borsuk's and Radon's theorem is presented. A related conjecture is formulated.

Słowa kluczowe

EN

admissible map; Borsuk-Ulam theorem

Kategorie tematyczne

• 47H04: Set-valued operators
• 05C35: Extremal problems
• 54H25: Fixed-point and coincidence theorems
• 52A20: Convex sets in n dimensions (including convex hypersurfaces)

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1995
• Tom: 15
• Numer: 2
• Strony: 187-190

Daty

wydano

1995

Twórcy

autor

Adam Idzik

• Institute of Computer Science, Polish Academy of Sciences, 21 Ordona, 01-237 Warsaw, Poland

Bibliografia

• [1] N. Alon, Some recent combinatorial applications of Borsuk-type theorems, In: Algebraic, Extremal and Metric Combinatorics (eds. M.M. Deza, P. Frankl, D.G. Rosenberg), Cambridge Univertsity Press, Cambridge (1988), 1-12.
• [2] N. Alon, Splitting necklaces, Advances in Math. 63 (1987), 247-253.
• [3] E.G. Bajmóczy and I. Bárány, On a common generalization of Borsuk's and Radon's theorem, Acta Math. Hung. (1979), 347-350.
• [4] I. Bárány, S.B. Shlosman and A. Szücs, On a topological generalization of a theorem of Tverberg, J. London Math. Soc. 33 (2) (1981), 158-164.
• [5] J. Dugundji and A. Granas, Fixed Point Theory, PWN - Polish Scientific Publishers, Warsaw 1982.
• [6] L. Górniewicz, Homological methods in fixed point theory of multi-valued maps, Dissertationes Math. 129 (1976), 1-71.
• [7] K. Gba and L. Górniewicz, On the Bourgin-Yang theorem for multi-valued maps I, Bull. Polish Acad. Sci. Math. 34 (1986), 315-322.
• [8] K.S. Sarkaria, A generalized van Kampen-Flores theorem, Proc. Amer. Math. Soc. 111 (1991), 559-565.
• [9] R.S. Simon, S. Spież and H. Toruńczyk, The existence of equilibria in certain games, separation for families of convex functions and a theorem of Borsuk-Ulam type, Mimeo. Inst. Math. Polish Acad. Sci. Warsaw 1994.
• [10] H. Steinlein, Borsuk's antipodal theorem and its generalizations and applications: A survey, In: Méthodes Topologiques en Analyse Non Linéaire, Coll. Sém. de Math. Sup., (ed. A. Granas), Univ. de Montréal Press, Montréal 95 (1985), 166-235.
• [11] H. Tverberg, A generalization of Radon's theorem, J. London Math. Soc. 41 (1966), 123-128.