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Shape Theory: Categorical Methods of Approximation

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Shape Theory: Categorical Methods of Approximation Cover

 

Synopses & Reviews

Publisher Comments:

This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.

A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and numerable covers, in addition to Morita's form of shape theory. Subsequent chapters explore Bénabou's theory of distributors, the theory of exact squares, Kan extensions, the notion of a stable object, and stability in an Abelian context. The text concludes with a brief description of derived functors of the limit functor theory—the concept that leads to movability and strong movability of systems—and illustrations of the equivalence of strong movability and stability in many contexts.

Synopsis:

This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. 1989 edition.

Synopsis:

This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. 1989 edition.

Table of Contents

Introduction
Advice to the reader
1. Borsuk's shape theory for compact metric spaces
2. Categorical shape theory
3. Shape theory for topological spaces
4. Distributors and shape theory
5. Functors between shape theories
6. Stability and movability
Appendix: Categorical shape theory and Pattern Recognition, a possible link
References
Index

Product Details

ISBN:
9780486466231
Author:
Cordier, J. M.
Publisher:
Dover Publications
Author:
Mathematics
Author:
Porter, T.
Subject:
Shape theory (Topology)
Subject:
General
Subject:
Physics
Subject:
Topology - General
Subject:
MATHEMATICS / Topology
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20080531
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
208
Dimensions:
9.25 x 6.13 in 0.6 lb

Related Subjects

Children's » Activities » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Topology
Science and Mathematics » Nature Studies » General
Young Adult » General

Shape Theory: Categorical Methods of Approximation New Trade Paper
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Product details 208 pages Dover Publications - English 9780486466231 Reviews:
"Synopsis" by ,
This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. 1989 edition.
"Synopsis" by ,
This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. 1989 edition.
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