Resolvability of groups - Ndhlalane, Mororiseng (University of the Witwatersrand, Johannesburg, 2020)
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.
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; SDG-17: Partnerships for the goals