The fundamental theorem of projective geometry states that a mapping from a projective space to itself whose range has a sufficient number of points in general position is a projective transformation possibly combined with a self-homomorphism of the underlying field. We obtain generalisations of this in many directions, dealing with the case where the mapping is only defined on an open subset of the underlying space, or a subset of positive measure, and dealing with many different spaces over many different rings.

Th. doct.--Informatique--Paris--Éc. polyt., 1996. / Bibliogr. p. 187-201. Résumé en anglais et en français. 1996 d'après la déclaration de dépôt légal.

Thesis (Ph. D.)--University of Chicago, 1932. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois." Bibliography: p. 55-56.

Thesis (Ph. D.)--Brigham Young University. Dept. of Mathematics, 2007. / Includes bibliographical references (p. 81-83).

Inaugural dissertation--Universität Regensburg, 1998.

Projective geometry: a boundless domain of countless fields where reals and imaginaries, finites and infinities, enter on equal terms, where the spirit delights in the artistic balance and symmeric interplay of a kind of conceptual and logical counterpoint, - an enchanted realm where thought is double and flows throughout in parallel stream.

No description available.

On introduit dans ce mémoire le plan projectif RP[indice supérieur 2] et certaines notions de géométrie projective telles que les coordonnées homogènes, les transformations projectives et le birapport. On s'intéresse plus particulièrement aux structures projectives convexes réelles sur une paire de pantalons. L'objectif est de paramétriser l'ensemble des classes d'équivalence de telles structures. On démontre que cet ensemble est de dimension huit et on identifie chaque structure projective à une configuration géométrique que nous visualiserons à l'aide du logiciel Mathematica. Finalement, on s'intéresse à l'effet des différents paramètres sur l'image de l'application développante, qui forme une région convexe du plan projectif.

Call number: LD2668 .T4 1938 W51 / Master of Science

We will discuss three ways to bound the chromatic number on a Cayley graph. 1. If the connection set contains information about a smaller graph, then these two graphs are related. Using this information, we will show that Cayley graphs cannot have chromatic number three. 2. We will prove a general statement that all vertex-transitive maximal triangle-free graphs on <i>n</i> vertices with valency greater than <i>n</i>/3 are 3-colourable. Since Cayley graphs are vertex-transitive, the bound of general graphs also applies to Cayley graphs. 3. Since Cayley graphs for abelian groups arise from vector spaces, we can view the connection set as a set of points in a projective geometry. We will give a characterization of all large complete caps, from which we derive that all maximal triangle-free cubelike graphs on 2ⁿ vertices and valency greater than 2ⁿ/4 are either bipartite or 4-colourable.