The prototype of a near-ring is the set of all self-maps of an additively written (but not necessarily abelian) group under pointwise addition and composition of maps. Moreover, any near-ring with unity can be embedded in a near-ring (with unity) of self-maps of some group. For this reason, a lot of research has been done on near-rings of maps. In 1979, Hofer [16] gave the study of near-rings of maps a topological avour by considering the near- ring of all continuous self-maps of a topological group. In this dissertation we consider some standard constructions of near-rings of maps on a group G and investigate these when G is a topological group and our near-ring consists of continuous maps.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nmmu/vital:10512 |
| Creators | Mogae, Kabelo |
| Publisher | Nelson Mandela Metropolitan University, Faculty of Science |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis, Doctoral, PhD |
| Format | vii, 89 leaves, pdf |
| Rights | Nelson Mandela Metropolitan University |
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