Modern Projective Geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
2000
|
| Series: | Mathematics and Its Applications
521 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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. |
| Physical Description: | 1 Online-Ressource (XVII, 363 p) |
| ISBN: | 9789401595902 9789048155446 |
| DOI: | 10.1007/978-94-015-9590-2 |
Staff View
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| 500 | |a 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. | ||
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Record in the Search Index
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
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| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9590-2 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401595902 9789048155446 |
| language | English |
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| spelling | Faure, Claude-Alain Verfasser aut Modern Projective Geometry by Claude-Alain Faure, Alfred Frölicher Dordrecht Springer Netherlands 2000 1 Online-Ressource (XVII, 363 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 521 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. Mathematics Algebra Matrix theory Combinatorics Geometry Quantum theory Linear and Multilinear Algebras, Matrix Theory Category Theory, Homological Algebra Quantum Physics Mathematik Quantentheorie Projektive Geometrie (DE-588)4047436-7 gnd rswk-swf Projektive Geometrie (DE-588)4047436-7 s 1\p DE-604 Frölicher, Alfred Sonstige oth https://doi.org/10.1007/978-94-015-9590-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Faure, Claude-Alain Modern Projective Geometry Mathematics Algebra Matrix theory Combinatorics Geometry Quantum theory Linear and Multilinear Algebras, Matrix Theory Category Theory, Homological Algebra Quantum Physics Mathematik Quantentheorie Projektive Geometrie (DE-588)4047436-7 gnd |
| subject_GND | (DE-588)4047436-7 |
| title | Modern Projective Geometry |
| title_auth | Modern Projective Geometry |
| title_exact_search | Modern Projective Geometry |
| title_full | Modern Projective Geometry by Claude-Alain Faure, Alfred Frölicher |
| title_fullStr | Modern Projective Geometry by Claude-Alain Faure, Alfred Frölicher |
| title_full_unstemmed | Modern Projective Geometry by Claude-Alain Faure, Alfred Frölicher |
| title_short | Modern Projective Geometry |
| title_sort | modern projective geometry |
| topic | Mathematics Algebra Matrix theory Combinatorics Geometry Quantum theory Linear and Multilinear Algebras, Matrix Theory Category Theory, Homological Algebra Quantum Physics Mathematik Quantentheorie Projektive Geometrie (DE-588)4047436-7 gnd |
| topic_facet | Mathematics Algebra Matrix theory Combinatorics Geometry Quantum theory Linear and Multilinear Algebras, Matrix Theory Category Theory, Homological Algebra Quantum Physics Mathematik Quantentheorie Projektive Geometrie |
| url | https://doi.org/10.1007/978-94-015-9590-2 |
| work_keys_str_mv | AT faureclaudealain modernprojectivegeometry AT frolicheralfred modernprojectivegeometry |