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### On the Maximum Theorem: A Constructive Analysis

**Abstract:**We examine the maximum theorem by Berge from the
point of view of Bishop style constructive mathematics. We will show
an approximate version of the maximum theorem and the maximum
theorem for functions with sequentially locally at most one maximum.

**References:**

[1] C. Berge. Topological Spaces. Macmillan, 1963.

[2] J. Berger, D. Bridges, and P. Schuster. The fan theorem and unique
existence of maxima. Journal of Symbolic Logic, 71:713-720, 2006.

[3] E. Bishop and D. Bridges. Constructive Analysis. Springer, 1985.

[4] K. Border. Fixed Point Theorems with Applications to Economics and
Game Theory. Cambridge University Press, 1985.

[5] D. Bridges and F. Richman. Varieties of Constructive Mathematics.
Cambridge University Press, 1987.

[6] D. Bridges and L. V╦å─▒t┬©╦ÿa. Techniques of Constructive Mathematics.
Springer, 2006.

[7] T. Ichiishi. Game Theory for Economic Analysis. Academic Press, 1983.