On Brouwer’s Fixed Point Theorem - Martynchuk, Nikolay (Topology Proceedings, 2022)
It is shown by Klaas Pieter Hart, Jan van Mill, and Roman Pol [Remarks on hereditarily indecomposable continua Topology Proc. 25 (2000), 179-206] that Brouwer’s fixed point theorem can be reduced to its 3 -dimensional case by using the hyperspace of a 2 -dimensional hereditarily indecomposable continuum. In this paper, we give a more direct and geometric argument that reduces the fixed point theorem to its 3 -dimensional version.