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＜電子ブック＞
Modern Projective Geometry / by Claude-Alain Faure, Alfred Frölicher
(Mathematics and Its Applications ; 521)

版	1st ed. 2000.
出版者	Dordrecht : Springer Netherlands : Imprint: Springer
出版年	2000
本文言語	英語
大きさ	XVII, 363 p : online resource
冊子体	Modern projective geometry / by Claude-Alain Faure and Alfred Frölicher
著者標目	*Faure, Claude-Alain author Frölicher, Alfred author SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Algebras, Linear LCSH:Discrete mathematics LCSH:Algebra, Homological LCSH:Quantum physics FREE:Geometry FREE:Linear Algebra FREE:Discrete Mathematics FREE:Category Theory, Homological Algebra FREE:Quantum Physics
一般注記	1. Fundamental Notions of Lattice Theory -- 2. Projective Geometries and Projective Lattices -- 3. Closure Spaces and Matroids -- 4. Dimension Theory -- 5. Geometries of degree n -- 6. Morphisms of Projective Geometries -- 7. Embeddings and Quotient-Maps -- 8. Endomorphisms and the Desargues Property -- 9. Homogeneous Coordinates -- 10. Morphisms and Semilinear Maps -- 11. Duality -- 12. Related Categories -- 13. Lattices of Closed Subspaces -- 14. Orthogonality -- List of Problems -- List of Axioms -- List of Symbols Projective geometry is a very classical part of mathematics and one might think that the subject is completely explored and that there is nothing new to be added. But it seems that there exists no book on projective geometry which provides a systematic treatment of morphisms. We intend to fill this gap. It is in this sense that the present monograph can be called modern. The reason why morphisms have not been studied much earlier is probably the fact that they are in general partial maps between the point sets G and G, noted ' 9 : G -- ~ G', i.e. maps 9 : D -4 G' whose domain Dom 9 := D is a subset of G. We give two simple examples of partial maps which ought to be morphisms. The first example is purely geometric. Let E, F be complementary subspaces of a projective geometry G. If x E G \ E, then g(x) := (E V x) n F (where E V x is the subspace generated by E U {x}) is a unique point of F, i.e. one obtains a map 9 : G \ E -4 F. As special case, if E = {z} is a singleton and F a hyperplane with z tf. F, then g: G \ {z} -4 F is the projection with center z of G onto F Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-94-015-9590-2

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