**"****How to Define a Topology in Spaces of **

**Real Analytic Functions?****"**

By

**ALEXANDER GONCHAROV**

**(BİLKENT UNIVERSITY)**

**Abstract: **There are two ways to define a natural topology in spaces of real analytic
functions: as a projective limit of inductive limits of certain Banach spaces
or as an inductive limit of projective
limits. Martineau (1966) showed that these topologies coincide. We consider some linear topological properties
of such spaces. The most interesting is that the space of real analytic functions
has no topological basis (Domanski, Vogt, 2000).

**Date: ****Tuesday, April 8, 2014**

**Time: ****15:40**

**Place: ****Mathematics Seminar Room,
SA-141**

Tea and cookies will be served before the
seminar.