Sehie Park
The National Academy of Sciences, Republic of Korea; Seoul 06579 and Department of Mathematical Sciences, Seoul National University, Seoul 08826, Korea.
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: Brouwer fixed point theorem, Sperner, KKM, Ky Fan, Grand KKM theory.
Park, S. (2022). Some new equivalents of the Brouwer fixed point theory. Advances in the Theory of Nonlinear Analysis and its Application , 6 (3), 300-309.