Department of Mathematics
Server

In this talk, topological modules are examined from a model theoretic perspective. Specifically, I attempt to expand the classical concepts of pure-embedding and pure-injectivity for modules to an analogous concept for topological modules. Historical definitions of pure embeddings for topological modules are explored as well as one of my own. Ultimately, the classic model theoretic techniques are inadequate for capturing the concept of pure-injectivity for topological modules. Insightful reasons are provided as to why these standard techniques fail.

In addition, when examining different topologies on the direct sum of modules, I developed a new approach for constructing the coproduct topology on the direct sum. This new approach uses different techniques from those already in the literature and this approach makes it less labour intensive to derive the coproduct topology's explicit form.

This talk is based on work presented in my Masters thesis, prepared under the direction of Dr. T. Kucera