Kurt Gödel Research Center

2012 seminar talk: Computable Analysis and Topology

Talk held by Matthias Schröder (KGRC) at the KGRC seminar on 2012-11-15.

Abstract

Computable Analysis investigates computability on the Euclidean space $\mathbb{R}$ and on related spaces. One approach to Computable Analysis is the Type Two Model of Effectivity (TTE). TTE provides a computational framework for non-discrete topological spaces with cardinality of at most card$(\mathbb{R})$.

We will give a short introduction to TTE. The basic tool of TTE are representations. A representation equips the objects of a given space with "names", which are infinite words. On these names the computation is performed. We discuss the property of admissibility as a well-behavedness criterion for representations. Then we characterise the class of topological spaces which can be equipped with an admissible representation. The ensuing category has a remarkably rich structure.