<p> In this thesis we examine a generalized notion of ordinary two dimensional affine and projective geometries The first six chapters deal very generally with coordinatization methods for these geometries and a direct construction of the analytic model for the affine case. The last two chapters are concerned with a discussion of these structures viewed as topological geometries. </p> / Thesis / Doctor of Philosophy (PhD)

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The important facts developed by the investigation are: Group III can be subdivided into two divisions without much injury to the delicacy of the individual tests. [See document for Scheme of Analysis For Group III] [See document for Diagramatic Scheme of Group III] The successful division of this group has eliminated the possibility of certain metals oxidizing during their initial precipitation and washing.* That the present of chromium precipitates an additional eleven per cent of zinc, but does not appreciably effect manganese. That different concentrations of ammonium hydroxide and ammonium chloride will precipitate varying amounts of zinc and manganese. The writer feels quite sure that his method requires less time and is less expensive than other methods.* / M.S.

The aim of this thesis is twofold. First, we investigate spaces defined by asserting that their nowhere dense subsets have certain properties. Secondly, we develop some techniques for the construction of topological spaces. We consider spaces where the nowhere dense sets are asserted to have some property P, calling such spaces boundary-P. We show that if there are no Lusin spaces then every compact boundary-metrizable space is metrizable. Boundary-separability is also studied and we show that if there are no L-spaces then every boundary-separable space is separable. By adapting the absolute dimension function of Arhangel'skii, we define the new concept of cohesion. We show that every compact cohesive and every Hausdorff, sequential cohesive space is scattered. However, we construct regular, crowded spaces of all finite cohesions though there are no regular spaces of transfinite cohesion. We consider too the preservation of cohesion under various mappings and under the formation of products. Turning to construction, we consider the class of compact monotonically normal spaces. It is well-known that it contains the class of spaces which are the continuous images of compact ordered spaces but it is still open as to whether they are actually distinct classes. Using Watson's resolutions, we give a method for constructing monotonically normal spaces. Though this also preserves continuous images of arcs, we show that it is because of a powerful result of Cornette rather than any trivial observation. We also examine more closely monotone normality in images of compact ordered spaces using the Collins-Roscoe structuring mechanism. From this, we extract a strong instance of the mechanism, linear chain (F), which is held by all images of ordered compacta and all proto-metrizable spaces and implies Junnila's concept of utter normality. Elementary submodels are an important tool in the construction of topological spaces. We develop a general method for applying them in varying circumstances and illustrate it by constructing three examples: Balogh's Q-set space, Rudin's normal but not collectionwise Hausdorff space and Balogh's small Dowker space.

We construct a co-analytic filter on the set of finite sequences of natural numbers, which allows us to obtain a strongly affine function of arbitrary Borel class from compact convex subset of locally convex space through single limit process (by this filter) applied to countable system of affine continuous functions. Conversely we show that function obtainted as result of such process is necessarily Borel and strongly affine. Further we generalize this method using metrizable reduction approach for Baire functions on non-metrizable spaces. Last chapter covers similar result for bi-analytic functions on separable metrizable spaces.

Le monde industriel est sans cesse confronté à des problèmes de choix. Une multitude de critères doit être pris en compte dans la résolution de ces derniers. Face à ces situations, les outils d’aide à la décision prennent tout leur sens. Nous utiliserons ici la méthode Analytic Hierarchic Process dans le domaine de la Production et plus particulièrement dans le cadre de l’ordonnancement d’une ligne de production de prothèses cardiovasculaires. Le paramétrage initial de cette méthode fait appel à l’évaluation d’un expert. Bien que ce dernier ait les connaissances nécessaires pour faire un paramétrage convenable, il n’en reste pas moins humain et introduira, même involontairement, une partie subjective dans ses décisions. L’ordonnancement en résultant ne sera donc pas forcément optimal. La réduction de cette subjectivité passe par l’utilisation d’une méta heuristique, de type algorithme génétique, pour améliorer ce paramétrage par l’exploration de solutions voisines à celles proposées par l’expert. / The industrial world is continually faced with problems of choices. Multitude of criterion must be taken into account in resolving them. Faced with these situations, the decision making tools give solutions. We will use the Analytic Hierarchy Process in the production field and especially in the scheduling of a cardio vascular prosthesis production line. The initial parameterization of this method involves the evaluation of an expert. Although he has the required knowledge to make a fitting setup, he is no less human and he will bring even unintentionally a subjective part in his decision. The resulting scheduling will therefore not necessarily be optimal. The reduction of the subjectivity can be done using a metaheuristic method, of genetic algorithm type, to improve this parameterization by exploring neighbouring solutions compared to those proposed by the expert.