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Boolean Partition Algebras, Joseph Anthony Van Name
Boolean Partition Algebras, Joseph Anthony Van Name
USF Tampa Graduate Theses and Dissertations
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.