Date of Award
The primary topic of this thesis is representation of vector lattices. The related theory of Boolean algebras is used as a tool to this end. In , Brown and Nakano present a theorem that establishes what we will call cr-representabihty for vector lattices in this thesis. We cast their proof in the light of the Boolean algebra of bands. Consequently, we show that it is the Loomis-Sikorski Theorem which makes their proof work. We then exploit this insight to study a-representability for greater cardinal numbers a. A primary goal of this thesis is to be self-contadned. As a result of this, the bulk of the text introduces definitions and theorems, as presented by other authors. We have liberally used existing theorems and proofs and give credit when ideas and/or exact proofs are borrowed. The novelty in our approach comes in connecting the work of Brown and Nakano with the Loomis-Sikorski Theorem and isolating our definition of or-representability.
Stephenson, Matthew Judson, "Alpha-Representability of Vector Lattices" (2010). Honors Theses. 2129.