{ "item_title" : "Infinite Homotopy Theory", "item_author" : [" H-J Baues", "A. Quintero "], "item_description" : "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- kjart6VT] 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, FreudenthalETR] 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 SiebenmannOFB],IS],DES] on non-compact manifolds.", "item_img_path" : "https://covers1.booksamillion.com/covers/bam/0/79/236/982/0792369823_b.jpg", "price_data" : { "retail_price" : "54.99", "online_price" : "54.99", "our_price" : "54.99", "club_price" : "54.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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