Resolvability of groups
Date
2020
Authors
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Publisher
University of the Witwatersrand, Johannesburg
Abstract
A topological group is called resolvable if it can be partitioned into two dense subsets. A group is absolutely resolvable if it can be partitioned into two subsets dense in any nondescript group topology. The aim of this dissertation is to give a unified exposition of some major results about resolvability of groups. In particular, we show that; 1. Every countable nondescript topological group not containing an open Boolean subgroup is resolvable, 2. Every infinite Abelian group not containing an infinite Boolean subgroup is absolutely resolvable.
Description
A dissertation submitted to Faculty of Mathematics in conformity with the requirements for the degree of Master of Science at University of Witwatersrand, Johannesburg. 2022
Keywords
Resolvable topogical groups, Omega-irresolvable groups, Absolute resovability