Dissertation/Thesis Abstract

Boolean Partition Algebras
by Van Name, Joseph, Ph.D., University of South Florida, 2013, 128; 3560193
Abstract (Summary)

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.

Indexing (document details)
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
Subjects: Mathematics
Keywords: Boolean algebras, Inverse limits, Partition algebras, Ultrafilters, Uniform spaces
Publication Number: 3560193
ISBN: 978-1-303-05946-9
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