Some new equivalents of the Brouwer fixed point theorem

Abstract

This is to recollect the equivalent formulations of the Brouwer fixed point theorem. We collect a large number of recently known sources of such equivalents. More recently, Jinlu Li obtained two fixed point theorems on newly defined quasi-point-separable topological vector spaces. His theorems extend the Tychonoff fixed point theorem on locally convex t.v.s. However, we note that his new theorems are logically equivalent to the Brouwer fixed point theorem. Consequently, we add up our large list of such equivalents.

Keywords

• Abstract convex space
• KKM theorem
• KKM class of multimaps
• $\mathfrak{A}_c^\kappa$
• $\mathfrak{B}$
• $\mathfrak{K}$
• $\mathfrak{KC}$
• $\mathfrak{KO}$

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