Relationentheoretische Charakterisierung teilweise angeordneter schwach-affiner Geometrien und ihrer Fernstrukturen / Relational characterization of partially ordered weak-affine spaces and their projected structures
The relational algebras 'affines Relativ' and 'affine Anordnungsalgebra' - relational structures with fixed arity used by Hans-Joachim Arnold for a synonymous algebraization of affine spaces and hilbertian ordered affine spaces without the need of the desarguesian axiom - are generalized for a common algebraic representation of any affine space including those with complete order. Therefore a new ordering is developed, which is independent from the axiom of Pasch and associated to the semiorder as described by e.g. Helga Tecklenburg under certain pappian conditions. The geometric structures obtained through projection from a certain point are also algebrized by a generalization of the 'projektive Multigruppe' and the 'projektive Punktalgebra mit Involution' leading to a generalized hessenbergian order of nearly projective spaces. Finally the whole theory is applied onto weak-affine spaces (still ensuring synonymity and orderability in the sense described here) and allows a characterization of those geometries having half or fully completed projections, i.e. projections with the axiom of Veblen, its generalizations or its ordered forms.
Advisor:Heinrich Wefelscheid; Hans-Joachim Arnold
Source Type:Master's Thesis
Keywords:mathematik universitaet duisburg essen
Date of Publication:08/15/2005