Infinite Homotopy Theory (Hardcover, 2001 ed.)

Compactness in topology and finite generation in algebra are nice properties to start with. However, the study of compact spaces leads naturally to non-compact spaces and infinitely generated chain complexes; a classical example is the theory of covering spaces. In handling non-compact spaces we must take into account the infinity behaviour of such spaces. This necessitates modifying the usual topological and algebraic cate gories to obtain "proper" categories in which objects are equipped with a "topologized infinity" and in which morphisms are compatible with the topology at infinity. The origins of proper (topological) category theory go back to 1923, when Kere kjart6 [VT] established the classification of non-compact surfaces by adding to orien tability and genus a new invariant, consisting of a set of "ideal points" at infinity. Later, Freudenthal [ETR] gave a rigorous treatment of the topology of "ideal points" by introducing the space of "ends" of a non-compact space. In spite of its early ap pearance, proper category theory was not recognized as a distinct area of topology until the late 1960's with the work of Siebenmann [OFB], [IS], [DES] on non-compact manifolds.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	K-Monographs in Mathematics, 6
Release date:	June 2001
First published:	2001
Authors:	H-J Baues • A Quintero
Dimensions:	234 x 156 x 19mm (L x W x T)
Format:	Hardcover
Pages:	296
Edition:	2001 ed.
ISBN-13:	978-0-7923-6982-0
Categories:	Books > Science & Mathematics > Mathematics > Topology > Algebraic topology Promotions
LSN:	0-7923-6982-3
Barcode:	9780792369820

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