Near vector spaces

[摘要] ENGLISH ABSTRACT:The preliminary material in Chapter 1 is included in order that this work be reasonably self-contained.The main aim of this thesis is to give an exposition of the theory of near vector spaces, as introduced by J. Andre [1]. This is done in the second chapter. Concepts such as an F-group and its quasi-kernel are defined and investigated. A near vector space is then defined in terms of these notions, after which the theory of near vector spaces is developed.Three examples are given in Chapter 3. Their quasi-kernels are investigated and, in each case, it is shown that the near vector space under consideration is not a vector space.Finally, in the fourth chapter, certain known results concerning linear transformations of finite-dimensional vector spaces are recalled. These notions are then investigated for certain near linear transformations of a 2-dimensional near vector space.

[发布机构] Stellenbosch University