Woensdag 5 december 2007
||Christopher J. Mulvey (University of Cambridge, University of Sussex)
||A Matter of Choice
||11:00 - 12:00
Vanaf kwart voor 11 is er koffie en thee in de binnenstraat
(voor de zaal).
In this talk we consider ways in which application of the Axiom of Choice may
be avoided by carefully chosen constructive argument of a geometric nature.
Taking the case of the Hahn-Banach theorem as an instance of this approach,
we examine how successive intrusions of the Axiom of Choice in its classical
proof may be removed to yield a constructive treatment of the theorem,
rephrased within the context of locales rather than topological space.
The constructive Hahn-Banach theorem obtained contains all the information
provided by the classical theorem, yet may be interpreted in many more
situations. In particular, in the presence of the Axiom of Choice it is
equivalent to the classical theorem.
Graduate students are encouraged to attend this talk.