Ndhlalane, Mororiseng2024-05-162024-05-162020https://hdl.handle.net/10539/38478A dissertation submitted to Faculty of Mathematics in conformity with the requirements for the degree of Master of Science at University of Witwatersrand, Johannesburg. 2022A 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.en© 2020 University of the Witwatersrand, JohannesburgResolvable topogical groupsOmega-irresolvable groupsAbsolute resovabilitySDG-17: Partnerships for the goalsDissertationUniversity of the Witwatersrand, Johannesburg