Fields institute,Room 210
Speaker: Mike Pawliuk
Title: Using T-sequences to create a robust family of topological groups.
Abstract: Using the methods of Protasov and Zelenyuk (“Topologies on Abelian Groups”, 1991) I will describe a method for constructing topological groups. We will focus on creating topologies on the integers (with the usual group operation) where non-trivial sequences converge to 0. Not all sequences in the Integers admit a T_2 group topology on the integers; those that do are called T-sequences.
We will examine three different aspects of T-sequences. First we will see that there are as many (different) T-sequences as possible, and that only certain types of chains of topologies given by T-sequences are possible. Then we will see that group topologies given by a (non-trivial) T-sequence are all examples of sequential spaces that are not Frechet-Urysohn. Finally, we will give a nice diagonalization technique that produces many topological groups on the integers that do not admit characters.
A cursory introduction can be found on my blog.