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Showing 1 to 10 of 10 for “"ultrafilter"”.
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Ultrafilters and compactification
In this thesis, we construct the ultrafilter space of a topological space using ultrafilters as points, study some of its properties and describe a method of generating compactifications through the ultrafilter space. As part of investigating some properties of the ultrafilter space, we show that …
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Topological Ramsey Spaces, Associated Ultrafilters, and Their Applications to the Tukey Theory of Ultrafilters and Dedekind Cuts of Nonstandard Arithmetic
… theory of arithmetic, and the Tukey theory of ultrafilters. The main results are broken into three parts.</p> <p>In the first part, we identify some new partition relations among finite trees and use them to answer an open question of Dobrinen; namely, "for n < omega, are the notions of Ramsey …
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Pseudocompactifications and pseudocompact spaces
… βX containing X such that every free hyperreal z-ultrafilter on X is fixed in αx. 2) αx is the largest subspace of βX containing X such that every point in αX - X is contained in a zero set which doesn't intersect X. The space αx also has the nice property that any subset of X which is closed and …
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Boolean ultrapowers
… theorem. By redefining the notion of a K-good ultrafilter on a Boolean algebra, Benda [1974] obtains a complete generalisation of a theorem of Keisler which states that an ultrapower is K-saturated iff the ultrafilter is K-good. Potthoff [1974] defines the notion of a limit Boolean ultrapower …
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Properties of ultraproduct spaces
… has an apparent defect in that it requires free ultrafilters which cannot be explicitly constructed, but this is not as serious as might be supposed. Many properties of the ultraproduct may be obtained with merely the knowledge that the ultra-filter used contains a given filter, and the utility …
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The performance of free chlorine and chlorine dioxide oxidation and/or alum coagulation for the removal of complexed Fe(II) from drinking water
… by the use of 0.2 um filters and 100K ultrafilters. Ultrafiltration and oxidation studies revealed that, at the DOC-to-iron ratios used for this research, not all of the Fe(II) in solution was actually complexed. Thus, oxidation studies represented the oxidation of uncomplexed Fe(II) to …
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Tripos models of Internal Set Theory
… Nelson models obtained from a choice of adequate ultrafilter and that mirror the constructions of classical Robinson nonstandard analysis, and the localic models for Transfer and Standardisation, which are obtained from any given open surjection of locales (e.g universal covers of topological …
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Human Adenoviruses As Indicators Of Faecal Contamination And Pathogen Indices In The Environment And Shellfish
… Method development included validation of an ultrafilter for virus concentration from water samples; real-time quantitative PCR (qPCR) assay development; evaluation of culture-qPCR using different cell lines; and assessment of guanidine hydrochloride to inhibit enterovirus growth in virus …
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AN INTRODUCTION TO BOOLEAN ALGEBRAS
<p>This thesis discusses the topic of Boolean algebras. In order to build intuitive understanding of the topic, research began with the investigation of Boolean algebras in the area of Abstract Algebra. The content of this initial research used a particular notation. The ideas of partially ordered …
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Ramsey Algebras and Ramsey Spaces
… proof of Hindman's theorem using idempotent ultrafilters. We study Ramsey algebras, which are structures that satisfy an analogue of Hindman's theorem. We show the existence of idempotent ultrafilters for Ramsey algebras under Martin's axiom, and the existence of idempotent ultrafilters for …