Brouwer's approximate fixed-point theorem is equivalent to Brouwer's fan theorem

Wim Veldman

pp. 277-299

in: Erik Palmgren, Krister Segerberg (eds), Logicism, intuitionism, and formalism, Berlin, Springer, 2009

Abstract

In a weak system for intuitionistic analysis, one may prove, using the Fan Theorem as an additional axiom, that, for every continuous function ø from the unit square U to itself, for every positive rational e, there exists x in U such that |ø(x) − x| < e. Conversely, if this statement is taken as an additional axiom, the Fan Theorem follows.

Cited authors

Brouwer Luitzen Egbertus Jan