Steven Leth : Some Examples of the use of nonstandard methods in continuum theory

Posted by Isaac Goldbring , part of the Departmental Colloquium.

At

April 24, 2015, 3 p.m.

In

SEO 636

Abstract

In this talk I will outline some applications of nonstandard methods to the study of compact, connected subsets of the plane. Nonstandard models allow for many complicated limiting properties of a set to be "actualized" in the nonstandard version of the set. This can make objects such as "pseudo-arcs" and other hereditarily indecomposable continua more intuitive to work with. Of particular interest are possible applications to sub-questions of the <i>plane fixed point problem</i>, which asks if every compact, connected subset of the plane that does not separate the plane has the fixed point property.