Some new equivalents of the Brouwer fixed point theorem
Sehie Park
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.
Topics & Concepts
Kakutani fixed-point theoremFixed-point theoremBrouwer fixed-point theoremMathematicsFixed-point propertyLefschetz fixed-point theoremDiscrete mathematicsSchauder fixed point theoremFixed pointPicard–Lindelöf theoremPure mathematicsMathematical analysisFixed Point Theorems AnalysisOptimization and Variational AnalysisAdvanced Optimization Algorithms Research