{"product_id":"infinite-homotopy-theory-9789401064934","title":"Infinite Homotopy Theory","description":"\u003cp\u003e • Author(s): H-J Baues\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Topology - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eCompactness 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45282718515351,"sku":"9789401064934","price":3639.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9789401064934.webp?v=1769302982","url":"https:\/\/atlanticbooks.com\/products\/infinite-homotopy-theory-9789401064934","provider":"Atlantic Books","version":"1.0","type":"link"}