Sinossi
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. F, then g: G \ {z} -4 F is the projection with center z of G onto F.
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Contenuti
Preface. Introduction. 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. Bibliography. List of Axioms. List of Symbols. Index.
Product Description
Book by Faure ClaudeAlain Frlicher Alfred
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Modern Projective Geometry
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This monograph develops projective geometries and provides a systematic treatment of morphisms. It introduces a new fundamental theorem and its applications describing morphisms of projective geometries in homogeneous coordinates by semilinear maps. Othe. Codice articolo 5969491
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Modern Projective Geometry (Mathematics and Its Applications, 521)
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Modern Projective Geometry
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This monograph develops projective geometries and provides a systematic treatment of morphisms. It introduces a new fundamental theorem and its applications describing morphisms of projective geometries in homogeneous coordinates by semilinear maps. Other topics treated include three equivalent definitions of projective geometries and their correspondence with certain lattices; quotients of projective geometries and isomorphism theorems; and recent results in dimension theory. 388 pp. Englisch. Codice articolo 9780792365259
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Modern Projective Geometry
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ISBN 10: 0792365259
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 388 pp. Englisch. Codice articolo 9780792365259
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9780792365259
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