A generalization of Tychonoff's fixed point theorem

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  1. [1]

    Begle, E. G.: A fixed point theorem. Ann. Math. (2)51, 544–550 (1950).

  2. [2]

    Bourbaki, N.: Espaces vectoriels topologiques, Chap. I, II. (Actual. Sci. et Industr. 1189.) Paris 1953.

  3. [3]

    Eilenberg, S., andD. Montgomery: Fixed point theorems for multi-valued transformations. Am. J. Math.68, 214–222 (1946).

  4. [4]

    Fan, K.: Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Nat. Acad. Sci. U. S.38, 121–126 (1952).

  5. [5]

    Glicksberg, I. L.: A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc. Am. Math. Soc.3, 170–174 (1952).

  6. [6]

    Kakutani, S.: A generalization of Brouwer's fixed-point theorem. Duke Math. J.8, 457–459 (1941).

  7. [7]

    Knaster, B., C. Kuratowski andS. Mazurkiewicz: Ein Beweis des Fixpunktsatzes fürn-dimensionale Simplexe. Fundamenta Math.14, 132–137 (1929).

  8. [8]

    Tychonoff, A.: Ein Fixpunktsatz. Math. Ann.111, 767–776 (1935).

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Dedicated to ProfessorMarston Morse

This work was supported by the U. S. Atomic Energy Commission at Argonne National Laboratory.

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Fan, K. A generalization of Tychonoff's fixed point theorem. Math. Ann. 142, 305–310 (1961) doi:10.1007/BF01353421

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  • Point Theorem
  • Fixed Point Theorem