Abstract
Star refinement, a fundamental concept in homology theory is also important in mathematical economics, as in the proof of Begle [1]'s fixed point theorem used in Nikaido [5]. Although Tukey [7]'s proof has been referred to by many articles, it contains a serious error. For applied fields like mathematical economics, it would be useful and necessary to create a complete version of the proof. In this paper, we first clearly point out the above problem in Tukey [7], and then provide the entire proof.
https://ror.org/035t8zc32 
