Equivalents of the Brouwer fixed point theorem are proved. They involve formulations either for the standard simplex or for the cube. Characterizations of continuous functions defined on the standard simplex are also presented. The famous Steinhaus chessboard theorem is generalized.
"Equivalent forms of the Brouwer fixed point theorem II." Topol. Methods Nonlinear Anal. 57 (1) 71 - 15, 2021. https://doi.org/10.12775/TMNA.2020.036