Woensdag 23 april 2008
Spreker: 
Bas Spitters (Radboud Universiteit)

Titel: 
The point of pointless topology

Tijd: 
11:00  12:00

Plaats: 
HG00.062

Vanaf kwart voor 11 is er koffie en thee in de
binnenstraat
(voor de zaal).
Abstract
Traditionally, a topological space is defined as a set of points together with
a certain distributive lattice of subsets. It turns out that most of the
theory can be developed using the lattice only. Logically, this may be seen
as a move from models to theories or as the move from individual choice
sequences to spreads in intuitionism. In this way, avoiding points allows us
to eliminate the axiom of choice from many proofs. This is crucial in our
recent work where we apply topos theory to the foundations of quantum theory,
but also connected to the implementation of the algebraic closure of a field
in
MAGMA, the use of modal logic in security and localization in
algebraic geometry.
This lecture will be studentfriendly as it assumes only very basic
knowledge of topology and lattice theory.