Date of Award
1-1-2023
Document Type
Dissertation
Degree Name
Ph.D. in Mathematics
First Advisor
Gerard Buskes
Second Advisor
Gerard Buskes
Third Advisor
Sandra Spiroff
School
University of Mississippi
Relational Format
dissertation/thesis
Abstract
We characterize when, for any infinite cardinal α, Fremlin’s Archimedean Riesz space tensor product of two Archimedean Riesz spaces is Dedekind α-complete. We provide an example of an ideal I in an Archimedean Riesz space E such that the Fremlin tensor product of I with itself is not an ideal in the Fremlin tensor product of E with itself. On the other hand, we present conditions for which the Fremlin tensor product of ideals is an ideal and that the Fremlin tensor product of projection bands is a projection band.
Lastly, we prove that the Carathéodory space of place functions on the free product of two Boolean algebras is Riesz isomorphic with the Fremlin tensor product of their respective Carathéodory spaces of place functions. This result is used to provide a solution to Fremlin’s problem 315Y(f) in [16] concerning completeness in the free product of Boolean algebras by applying our results on the Fremlin tensor product to Carathéodory spaces of place functions.
Recommended Citation
Thorn, Page, "On the Tensor Product of Archimedean Riesz Spaces" (2023). Electronic Theses and Dissertations. 2590.
https://egrove.olemiss.edu/etd/2590