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
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/21043 |
| Date | 16 September 2016 |
| Creators | Lethulwe, Neo |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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