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Infinite Homotopy Theory (in English)
H-J Baues
(Author)
·
A. Quintero
(Author)
·
Springer
· Paperback
Infinite Homotopy Theory (in English) - Baues, H-J ; Quintero, A.
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Synopsis "Infinite Homotopy Theory (in English)"
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.
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The book is written in English.
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