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.
| Identifer | oai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-5796 |
| Date | 01 January 2013 |
| Creators | Van Name, Joseph Anthony |
| Publisher | Scholar Commons |
| Source Sets | University of South Flordia |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Graduate Theses and Dissertations |
| Rights | default |
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