Shape Theory

Categorical Methods of Approximation

By: J M Cordier, T Porter

Write A Review

Paperback | 19 May 2008

At a Glance

Paperback
207 Pages

Dimensions(cm)
22.86 x 15.88 x 1.27

Paperback

RRP $24.15

$23.75

or 4 interest-free payments of $5.94 with

Ships in 5 to 7 business days

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 Benabou'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.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Topology Science Science in General Physics

Introduction	p. 7
Advice to the reader	p. 13
Borsuk's shape theory for compact metric spaces	p. 15
Absolute retracts and absolute neighbourhood retracts	p. 17
Borsuk's shape theory	p. 19
Fundamental sequences and inverse systems of ANRs	p. 22
Historical Note	p. 27
Categorical shape theory	p. 28
Shape theory	p. 28
Examples of shape theories	p. 32
Pro-objects, procategories and proadjoints	p. 36
Shape theory and procategories	p. 53
Kan extensions and Holsztynski's shape functor	p. 58
Codensity monads	p. 64
Historical Note	p. 69
Shape theory for topological spaces	p. 70
Simplicial complexes and numerable covers	p. 70
Shape for topological spaces	p. 74
Comparison of the shape theories of Borsuk, Fox, Mardesic-Segal and Mardesic	p. 77
Historical Note	p. 85
Distributors and shape theory	p. 86
The bicategory, Dist	p. 86
Codensity monads and Kleisli categories in Dist	p. 98
Shape theories and distributors	p. 102
Notes on sources	p. 111
Functors between shape theories	p. 112
Change of models	p. 112
Absolute Kan extensions	p. 114
Exact squares	p. 127
Examples and applications of exact squares	p. 133
Some topological examples of exact squares with applications to suspensions of (pointed) spaces	p. 140
Notes on sources	p. 153
Stability and movability	p. 154
The interpretation of categorical notions in a shape category	p. 154
Stability	p. 157
Reindexing lemmas	p. 162
Stability in pro-Abelian categories	p. 166
The derived functors of Lim	p. 175
Movability and Mittag-Leffler	p. 178
Strong movability	p. 189
Notes on sources	p. 196
Categorical shape theory and Pattern Recognition, a possible link	p. 198
References	p. 201
Index	p. 205
Table of Contents provided by Ingram. All Rights Reserved.

Shape Theory

Categorical Methods of Approximation

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Physics

Quantum 2.0

The Past, Present, and Future of Quantum Physics

Astrophysics for People in a Hurry

Black Holes

The key to understanding the universe

The Universe

The Book Of The BBC TV Series Presented By Professor Brian Cox

A Short History of Nearly Everything 2.0

The Breath of the Gods

The History and Future of the Wind

A Periodic Tale: the bestselling life-long story of Australia's favourite science champion Dr Karl Kruszelnicki, shortlisted for the ABIA Biography

My Sciencey Memoir

More and More and More

An All-Consuming History of Energy

The Elements of Marie Curie

How the Glow of Radium Lit a Path for Women in Science

Just Visiting This Planet

Merlin Answers More Questions about Everything under the Sun, Moon and Stars

Seven Brief Lessons on Physics

Anniversary Edition

Brief Answers to the Big Questions

Final book from Stephen Hawking

"Surely You're Joking, Mr. Feynman!"

Adventures of a Curious Character

The Invisible Rainbow

A History of Electricity and Life

Seven Brief Lessons on Physics

Stargazing for Beginners

Explore the Wonders of the Night Sky

Quantum Body

The New Science of Living a Longer, Healthier, More Vital Life

The Biggest Ideas in the Universe 2

Quanta and Fields

Green and Sustainable Synthesis of Iron Oxide-Based Nanomaterials for Energy and Environmental Applications

Metal Oxides

Handbook of Power Electronics in Smart Grids and Intelligent Energy

Biofuel Perspectives

Methanol and Ethanol in Combustion Engines from Production to Practical Application

The Art of Physics

How ideas from science can transform your life

The Art of Electronics

3rd edition improved

Blue Machine

How the Ocean Shapes Our World

This product is categorised by