Brouwer's approximate fixed-point theorem is equivalent to Brouwer's fan theorem
pp. 277-299
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.
Publication details
Published in:
Palmgren Erik, Segerberg Krister (2009) Logicism, intuitionism, and formalism: what has become of them?. Dordrecht, Springer.
Pages: 277-299
DOI: 10.1007/978-1-4020-8926-8_14
Full citation:
Veldman Wim (2009) „Brouwer's approximate fixed-point theorem is equivalent to Brouwer's fan theorem“, In: E. Palmgren & K. Segerberg (eds.), Logicism, intuitionism, and formalism, Dordrecht, Springer, 277–299.