Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Separation and von Neumann intersection theorems

Author: Shiow Yu Chang
Journal: Proc. Amer. Math. Soc. 112 (1991), 1149-1152
MSC: Primary 54H25; Secondary 49J35, 90D05
MathSciNet review: 1070512
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give some separation theorems to extend the intersection theorem of von Neumann, Fan, and others, omitting hypotheses of convexity and local convexity for one of the coordinate spaces.

References [Enhancements On Off] (What's this?)

  • [1] K. Fan, Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 121-126. MR 0047317 (13:858d)
  • [2] I. L. Glicksberg, A further generalization of the Kukutani fixed point theorem, with application to Nash equilibrium points, Proc. Amer. Math. Soc. 3 (1952), 170-174. MR 0046638 (13:764g)
  • [3] Chung-Wei Ha, Minimax and fixed point theorem, Math. Ann. 248 (1980), 73-77. MR 569411 (81i:47058)
  • [4] S. Kukutani, A generalization of Brouwer's fixed point theorem, Duke Math. J. 7 (1941), 457-459.
  • [5] J. von Neumann, Zur Theorie der Gesellschaftsspiele, Math. Ann. 100 (1928), 295-320. MR 1512486
  • [6] -, Uber ein okonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes, Ergeb. eines Math. 8 (1937), 73-83.
  • [7] N. C. Yannelies and N. D. Prabhakar, Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econom. 12 (1983), 233-245. MR 743037 (87h:90061a)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54H25, 49J35, 90D05

Retrieve articles in all journals with MSC: 54H25, 49J35, 90D05

Additional Information

Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society