Borsuk-Ulam type theorems

Adam Idzik

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1995)

  • Volume: 15, Issue: 2, page 187-190
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Adam Idzik. "Borsuk-Ulam type theorems." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 15.2 (1995): 187-190. <http://eudml.org/doc/275984>.

@article{AdamIdzik1995,
abstract = {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.},
author = {Adam Idzik},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {admissible map; Borsuk-Ulam theorem; theorem of Bajmóczy and Bárány; generalization of Borsuk's and Radon's theorem},
language = {eng},
number = {2},
pages = {187-190},
title = {Borsuk-Ulam type theorems},
url = {http://eudml.org/doc/275984},
volume = {15},
year = {1995},
}

TY - JOUR
AU - Adam Idzik
TI - Borsuk-Ulam type theorems
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1995
VL - 15
IS - 2
SP - 187
EP - 190
AB - 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.
LA - eng
KW - admissible map; Borsuk-Ulam theorem; theorem of Bajmóczy and Bárány; generalization of Borsuk's and Radon's theorem
UR - http://eudml.org/doc/275984
ER -

References

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  1. [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. [2] N. Alon, Splitting necklaces, Advances in Math. 63 (1987), 247-253. 
  3. [3] E.G. Bajmóczy and I. Bárány, On a common generalization of Borsuk's and Radon's theorem, Acta Math. Hung. (1979), 347-350. Zbl0446.52010
  4. [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. Zbl0453.55003
  5. [5] J. Dugundji and A. Granas, Fixed Point Theory, PWN - Polish Scientific Publishers, Warsaw 1982. 
  6. [6] L. Górniewicz, Homological methods in fixed point theory of multi-valued maps, Dissertationes Math. 129 (1976), 1-71. 
  7. [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. Zbl0613.55001
  8. [8] K.S. Sarkaria, A generalized van Kampen-Flores theorem, Proc. Amer. Math. Soc. 111 (1991), 559-565. Zbl0722.57007
  9. [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. Zbl0843.90143
  10. [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. Zbl0573.55003
  11. [11] H. Tverberg, A generalization of Radon's theorem, J. London Math. Soc. 41 (1966), 123-128. Zbl0131.20002

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