Graduation Year
2013
Document Type
Dissertation
Degree
Ph.D.
Degree Granting Department
Mathematics and Statistics
Major Professor
Vilmos Totik
Keywords
Boolean Algebra, Inverse Limit, Partition, Ultrafilter, Uniform Space
Abstract
A Boolean partition algebra is a pair $(B,F)$ where $B$ is a Boolean
algebra and $F$ is a filter on the semilattice of partitions of $B$ where $\bigcup F=B\setminus\{0\}$. In this dissertation, we shall investigate the algebraic theory of Boolean partition algebras and their connection with uniform spaces. In particular, we shall show that the category of complete non-Archimedean uniform spaces
is equivalent to a subcategory of the category of Boolean partition algebras, and notions such as supercompleteness
of non-Archimedean uniform spaces can be formulated in terms of Boolean partition algebras.
Scholar Commons Citation
Van Name, Joseph Anthony, "Boolean Partition Algebras" (2013). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/4599
