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- About this book
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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.
- Table of contents (14 chapters)
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Fundamental Notions of Lattice Theory
Pages 1-24
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Projective Geometries and Projective Lattices
Pages 25-53
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Closure Spaces and Matroids
Pages 55-79
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Dimension Theory
Pages 81-106
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Geometries of Degree n
Pages 107-125
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Table of contents (14 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Modern Projective Geometry
- Authors
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- Claude-Alain Faure
- Alfred Frölicher
- Series Title
- Mathematics and Its Applications
- Series Volume
- 521
- Copyright
- 2000
- Publisher
- Springer Netherlands
- Copyright Holder
- Springer Science+Business Media Dordrecht
- eBook ISBN
- 978-94-015-9590-2
- DOI
- 10.1007/978-94-015-9590-2
- Hardcover ISBN
- 978-0-7923-6525-9
- Softcover ISBN
- 978-90-481-5544-6
- Edition Number
- 1
- Number of Pages
- XVII, 363
- Topics
