Boolean Partition Algebras

• Main Author: Van Name, Joseph
• Language: EN
• Published: University of South Florida 2013
• Subjects: Mathematics
• Online Access: http://pqdtopen.proquest.com/#viewpdf?dispub=3560193

<p>A Boolean partition algebra is a pair (<i>B</i>, <i>F </i>) where <i>B</i> is a Boolean algebra and <i>F</i> is a filter on the semilattice of partitions of <i>B</i> where [special characters omitted] <i>F</i> = <i>B</i> \ {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.</p>