A Further Improvement of a Minimax Theorem of Borenshtein and Shul'Man

Abstract

Ten years ago, Borenshtein and Shul'man proved a minimax theorem for real-valued functions defined in the product of a compact metric space and a real interval. Recently, this result has been improved, in a remarkable way, by J. Saint Raymond who, however, kept compactness and metrizability of the abstract factor space. In this paper, I improve Saint Raymond's result assuming that the abstract factor space be simply a topological space.

Keywords: Analysis, Geometry and Topology, Applied Mathematics, Pure_mathematics/0108007