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Affine Geometry: Incidence with Parallelism (IP)
2015This brief chapter introduces the notion of parallelism, discusses the two forms of the parallel axiom, defines affine geometry, and proves five elementary theorems relating to intersecting planes and parallel lines.
Edward John Specht +3 more
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Infinite dimensions for ordered incidence geometry
Journal of Geometry, 1989In J. Geom. 30, 103-122 (1988; Zbl 0629.51013), \textit{A. Ben-Tal} and \textit{A. Ben-Israel} have set up an abstract conexity theory based on the notions of incidence, order, affine hull and dimension. Although they incorporate the case of infinite dimensions into their axiomatic setting, their work mainly refers to finite dimensional geometries and ...
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Incidence loops and their geometry
1992Publisher Summary This chapter discusses the concept of incidence loops and their geometry. An incidence group (P, L,·) is a group (P,·) together with a structure (P, L) of an incidence space such that both structures are compatible. The notion of incidence group can be generalized by weakening the assumptions concerning the algebraic structure of P;
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Generalized doubling for incidence geometries
2006An (incidence) geometry is a structure (X, , I, t) in which (X, ) is a simple graph and t is a surjective map from X onto a set I such that the pre-images t?1(i) are cocliques for each i 2 I. The rank of the geometry is the cardinality of the set I. The vertices of the graph underlying a geometry are called elements of the geometry.
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