Browsing by Author "Ndhlalane, Mororiseng"

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    Resolvability of groups
    (University of the Witwatersrand, Johannesburg, 2020) Ndhlalane, Mororiseng
    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.