UID:
edocfu_9958087978102883
Format:
1 online resource (383 p.)
ISBN:
1-283-52584-4
,
9786613838292
,
0-08-095428-6
Series Statement:
North-Holland mathematical library ; volume 22
Content:
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.
Note:
Description based upon print version of record.
,
Front Cover; Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories; Copyright Page; Preface; Contents; Introduction; Chapter I. Preliminaries; 1. Relations, algebraic operations, homomorphisms; 2. Monoids and concrete monoids; 3. Categories, functors, transformations; 4. Concrete categories; 5. Some important concrete categories; 6. Embeddings; 7. Two easy but important embeddings; 8. The representation problems; 9. Bibliographical remarks; Chapter II. Basic Embeddings; 1. Three obvious realizations; 2. Two important extensions
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3. Rigid binary relations4. Rigid symmetric binary relations; 5. Graph is alg-universal. Consequences; 6. Assumption (M) and strong embedding of S(P-) into Graph; 7. Strong embedding of S(P+) into S(P-); 8. Bibliographical remarks; Chapter III. Universality of S(P+); 1. Strong embedding of S(P+ , . . ., P+) into S(P+); 2. Representations of thin categories; 3. Categories I(F; (T,〈=)) and realizations of concrete categories; 4. S(P+) is universal; 5. Bibliographical remarks; Chapter IV. Combinatorics; 1. Graphs, symmetric graphs, undirected graphs
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2. The "arrow construction" in its simplest form3. Two applications of the arrow construction: Symmetric graphs and acyclic graphs; 4. More about undirected graphs; 5. Partially ordered sets; 6. Graphs with strong homomorphisms; 7. Graphs with loops; 8. Sets with two equivalences; 9. A technical lemma; 10. On a problem by S. Ulam; 11. Bibliographical remarks; Chapter V. Algebra; 1. Some easy results; 2. Embeddings into the categories of semigroups and monoids; 3. Categories of rings; 4. Categories of lattices; 5. Unary algebras; 6. Categories of small categories
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7. Remarks on categories of functors8. Bibliographical remarks; Chapter VI. Topology; 1. An elementary result about T0-spaces; 2. Some special mappings. Quontients and sums of metric spaces; 3. The functors M, Mo, M, Mo, Ms, and Mu; 4. Some full embeddings into categories of metric spaces; 5. Labeled topologized graphs. The functor P; 6. Construction of sufficiently rigid basec and fundamental classes; 7. Some strong embeddings into categories of metric spaces; 8. Some universal categories of metric spaces; 9. Negative results on open and locally one-to-one mappings
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10. Techniques for T1-spaces11. Alg-universal categories of T1-spaces; 12. Strong embeddings into categories of T1-spaces; 13. The category of T1-spaces and their open continuous mappings is universal; 14. Rigid spaces and stiff classes of spaces; 15. The category of paracompact spaces is almost universal; 16. Compact Hausdorff spaces; 17. Some negative results; 18. Bibliographical remarks; Chapter VII. Strong Embeddings and Strongly Algebraic Categories; 1. Strong embeddings of categories S(F) into S(P+) and Graph; 2. Which concrete categories are strongly embeddable into S(P+)
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3. Strong universality
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English
Additional Edition:
ISBN 0-444-85083-X
Language:
English
