{"product_id":"the-theory-of-cluster-sets-paperback-9780521604819","title":"The Theory of Cluster Sets (Paperback) 9780521604819","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Theory of Cluster Sets\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAn introduction to the theory of cluster sets, a branch of topological analysis.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eE. F. Collingwood (Author), A. J. Lohwater (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521604819, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 3 June 2004\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e224 pages\u003cbr\u003e21.5 x 14 x 1.4 cm, 0.294 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe book provides an introduction to the theory of cluster sets, a branch of topological analysis which has made great strides in recent years. The cluster set of a function at a particular point is the set of limit values of the function at that point which may be either a boundary point or (in the case of a non-analytic function) an interior point of the function's domain. In topological analysis, its main application is to problems arising in the theory of functions of a complex variable, with particular reference to boundary behaviour such as the theory of prime ends under conformal mapping. An important and novel feature of the book is the discussion of more general applications to non-analytic functions, including arbitrary functions. The authors assume a general familiarity with classical function theory but include the more specialised material required for the development of the theory of cluster sets, so making the treatment accessible to graduate students.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 1. Introduction\u003cbr\u003e 2. Functions analytic in a circular disc\u003cbr\u003e 3. Topics in the theory of conformal mapping\u003cbr\u003e 4. Intrinsic properties of cluster sets\u003cbr\u003e 5. Cluster sets of functions analytic in the unit disc\u003cbr\u003e 6. Boundary theory in the large\u003cbr\u003e 7. Boundary theory in the small\u003cbr\u003e 8. Further boundary properties of functions meromorphic in the disc. classification of singularities\u003cbr\u003e 9. Prime ends\u003cbr\u003e Bibliography\u003cbr\u003e Index of symbols\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46129229889816,"sku":"9780521604819","price":37.65,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521604819i.jpg?v=1691666399","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-theory-of-cluster-sets-paperback-9780521604819","provider":"Freshly Printed Books","version":"1.0","type":"link"}