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Showing 1 to 17 of 17 for “"Ultrafilters"”.
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Ultrafilters and compactification
… 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 the ultrafilter space forms a …
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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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Construction of Deligne Categories through ultrafilters and its applications
… Deligne categories in this study is the one of ultrafilters and ultraproducts. As will be shown in our work, this approach turns out to be a very powerful one. Especially if one wants to solve such representation-theoretic problems as presented by P.Etingof in his papers on "Representation …
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Topological Dynamics of Automorphism Groups of omega-homogeneous Structures via Near Ultrafilters
… universal minimal flow in the language of near ultrafilters. We apply this viewpoint to generalize results of Kechris, Pestov and Todorčević about a connection between groups of automorphisms of structures and structural Ramsey theory from countable to uncountable structures. This allows us to …
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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 …
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Nonstandard analysis based calculus
… of Nonstandard Analysis, including the theory of ultrafilters, and the formal construction of the Hyperreals.
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Nonstandard analysis based calculus
… of Nonstandard Analysis, including the theory of ultrafilters, and the formal construction of the Hyperreals.
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Forcing in Analysis and Combinatorics
… on selective or semiselective coideals and ultrafilters.
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The performance of potassium permanganate and hydrogen peroxide oxidation and/or alum coagulation in the removal of complexed FE(II) from drinking water
… through the use of 0.2 urn filters and 100K ultrafilters. Results from oxidation and ultrafiltration studies indicated incomplete complexation of the Fe(II) by DOC in solution. Following the addition of either oxidant, uncomplexed Fe(II) was oxidized to Fe (III) which was either complexed by …
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The effects of rainfall runoff from urban and rural watersheds on trihalomethane precursors in streams
… through 500, 1000, 5000, 10000, and 30000 dalton ultrafilters and were then chlorinated to determine the THM-formation potential based on the total organic concentration of the water fraction. From the data collected, it was shown that seasonal changes influenced the TOC and THM-precursor loadings …
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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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Martingale Convergence Techniques in Noncommutative Integration
… the study of almost everywhere convergence using ultrafilters, and the martingale structure of the infinitely iterated tower of ultrapowers.
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Boolean ultrapowers
… the notion of the Rudin-Keisler ordering to ultrafilters on complete Boolean algebras, and prove that by using this definition, Blass' Characterisation Theorem can be generalised for Boolean ultrapowers.
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The characterization of dissolved organic material in natural waters and the phase-change behavior of organic matter during chemical coagulation
… fraction on each other during coagulation. Ultrafilters (30K and 100K nominal molecular weight cutoff) were utilized to analyze the phase-change behavior of DOM during coagulation. Results indicated the coagulation pH affected the removal of the organic acidic fractions but not the neutral …
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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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Topological Dynamics On Compact Phase Spaces
… and treat its compactification as the set of ultrafilters on $N$ and the extended action as that of $\beta N$. In so doing we will present results which relate notions of proximality and almost periodicity in a dynamical system to combinatorially rich central subsets of $N$. In lieu of an …