{"product_id":"convergence-structures-and-applications-to-functional-analysis-hardcover","title":"Convergence Structures and Applications to Functional Analysis - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eR. Beattie\u003c\/b\u003e (Author), \u003cb\u003eHeinz-Peter Butzmann\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eFor many, modern functional analysis dates back to Banach's book  Ba32]. Here, such powerful results as the Hahn-Banach theorem, the open-mapping theorem and the uniform boundedness principle were developed in the setting of complete normed and complete metrizable spaces. When analysts realized the power and applicability of these methods, they sought to generalize the concept of a metric space and to broaden the scope of these theorems. Topological methods had been generally available since the appearance of Hausdorff's book in 1914. So it is surprising that it took so long to recognize that they could provide the means for this generalization. Indeed, the theory of topo- logical vector spaces was developed systematically only after 1950 by a great many different people, induding Bourbaki, Dieudonne, Grothendieck, K the, Mackey, Schwartz and Treves. The resulting body of work produced a whole new area of mathematics and generalized Banach's results. One of the great successes here was the development of the theory of distributions. While the not ion of a convergent sequence is very old, that of a convergent fil- ter dates back only to Cartan  Ca]. And while sequential convergence structures date back to Frechet  Fr], filter convergence structures are much more recent:  Ch],  Ko] and  Fi]. Initially, convergence spaces and convergence vector spaces were used by  Ko],  Wl],  Ba],  Ke64],  Ke65],  Ke74],  FB] and in particular  Bz] for topology and analysis.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 264\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.68 x 9.9 x 6.38 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e March 31, 2002\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47336832729337,"sku":"9781402005664","price":178.18,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/t5tpbgyeuR9781402005664.webp?v=1769671358","url":"https:\/\/bookscloud.io\/products\/convergence-structures-and-applications-to-functional-analysis-hardcover","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}