giovedi' 17-03-2005 (15:00) - Sala Riunioni Steven Leth (Univ. of Northern Colorado, USA) : Examples of the use of nonstandard methods in geometric topology and in combinatorial number theory

Abstract: We will begin with a short proof that every simple closed curve in the plane can be approximated arbitrarily closely by a simple closed polygon. We will then look at how density conditions on a sequence of natural numbers can translate to Lebesgue measure properties of the reals via a nonstandard model.This allows us to prove (standard) theorems about the existence of arithmetic progressions or "nearly" arithmetic progressions in the sequence.

Giulia Curciarello Segreteria Didattica tel: 050-2213219 e-mail curciare@dm.unipi.it

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