A research project submitted in partial fulfilment of the requirements for the degree of Master of Science School of Mathematics, University Of Witwatersrand 18 May 2016 / A topological group is called resolvable (ω-resolvable) if it can be partitioned into two (into ω) dense subsets and absolutely resolvable (absolutely ω-resolvable) if it can be partitioned into two (into ω) subsets dense in every nondiscrete group topology. These notions have been intensively studied over the past 20 years. In this dissertation some major results in the field are presented. In particular, it is shown that (a) every countable nondiscrete topological group containing no open Boolean subgroup is ω-resolvable, and (b) every infinite Abelian group containing no infinite Boolean subgroup is absolutely ω-resolvable. / M T 2016

Inaug.-diss.--Münster.

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Hung Cheung Yan. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaves 28-29.

Chan, Wai-Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 52-53). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.iii / Introduction --- p.iv / Chapter 1 --- Preliminaries --- p.1 / Chapter 1.1 --- C*-algebras --- p.1 / Chapter 1.2 --- Topological groups --- p.8 / Chapter 2 --- Property T for topological groups --- p.18 / Chapter 2.1 --- Definitions and some basic properties --- p.18 / Chapter 2.2 --- Hereditary properties --- p.23 / Chapter 2.3 --- A characterization for property T --- p.26 / Chapter 2.4 --- Examples --- p.32 / Chapter 3 --- Property T for C*-algebras --- p.34 / Chapter 3.1 --- Countable discrete groups and their group C*- algebras --- p.34 / Chapter 3.2 --- Property T and nuclearity --- p.46 / Bibliography --- p.52

Thesis (Ph. D.)--Oregon State University, 1969. / Typescript. Includes bibliographical references (leaf 69). Also available on the World Wide Web.

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1931. / Vita. "Sonderabdruck aus der "Mathematischen zeitschrift", Band 33, Heft 5"--T.p. verso. Includes bibliographical references.

The investigation of this paper is introduced by describing an important collection of morphisms between two topological groupoids. Characterizations of the different types of morphisms of this collection will be formulated in order to facilitate the construction and the classication of the various morphisms considered. In addition, the relationships existing among the various members of this collection will be determined.

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