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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 [special characters omitted] F = B \ {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.
| Advisor: | Totik, Vilmos |
| Commitee: | Hou, Xiang-Dong, Khavinson, Dmitry, McColm, Gregory |
| School: | University of South Florida |
| Department: | Mathematics and Statistics |
| School Location: | United States -- Florida |
| Source: | DAI-B 74/08(E), Dissertation Abstracts International |
| Source Type: | DISSERTATION |
| Subjects: | Mathematics |
| Keywords: | Boolean algebras, Inverse limits, Partition algebras, Ultrafilters, Uniform spaces |
| Publication Number: | 3560193 |
| ISBN: | 978-1-303-05946-9 |
