{"product_id":"category-and-measure-infinite-combinatorics-topology-and-groups-hardback-9780521196079","title":"Category and Measure; Infinite Combinatorics, Topology and Groups (Hardback) 9780521196079","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eCategory and Measure\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eInfinite Combinatorics, Topology and Groups\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eThe continuous structure of topological spaces is examined from the viewpoints of category and measure, with the former being paramount.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eN. H. Bingham (Author), Adam J. Ostaszewski (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521196079, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 23 January 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e345 pages\u003cbr\u003e23.5 x 15.9 x 2.4 cm, 0.64 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\"\u003eTopological spaces in general, and the real numbers in particular, have the characteristic of exhibiting a 'continuity structure', one that can be examined from the vantage point of Baire category or of Lebesgue measure. Though they are in some sense dual, work over the last half-century has shown that it is the former, topological view, that has pride of place since it reveals a much richer structure that draws from, and gives back to, areas such as analytic sets, infinite games, probability, infinite combinatorics, descriptive set theory and topology. Keeping prerequisites to a minimum, the authors provide a new exposition and synthesis of the extensive mathematical theory needed to understand the subject's current state of knowledge, and they complement their presentation with a thorough bibliography of source material and pointers to further work. The result is a book that will be the standard reference for all researchers in the area.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePrologue. Regular variation\u003cbr\u003e 1. Preliminaries\u003cbr\u003e 2. Baire category and related results\u003cbr\u003e 3. Borel sets, analytic sets and beyond: $Delta^1_2$\u003cbr\u003e 4. Infinite combinatorics in $mathbb{R}^n$: shift-compactness\u003cbr\u003e 5. Kingman combinatorics and shift-compactness\u003cbr\u003e 6. Groups and norms: Birkhoff–Kakutani theorem\u003cbr\u003e 7. Density topology\u003cbr\u003e 8. Other fine topologies\u003cbr\u003e 9. Category-measure duality\u003cbr\u003e 10. Category embedding theorem and infinite combinatorics\u003cbr\u003e 11. Effros' theorem and the cornerstone theorems of functional analysis\u003cbr\u003e 12. Continuity and coincidence theorems\u003cbr\u003e 13. * Non-separable variants\u003cbr\u003e 14. Contrasts between category and measure\u003cbr\u003e 15. Interior point theorems: Steinhaus–Weil theory\u003cbr\u003e 16. Axiomatics of set theory\u003cbr\u003e Epilogue. Topological regular variation\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Calculus \u0026amp; mathematical analysis [\u003ca title=\"See our other books on Calculus \u0026amp; mathematical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Calculus%20\u0026amp;%20mathematical%20analysis%20%5BPBK%5D%22\"\u003ePBK\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52475166458136,"sku":"9780521196079","price":82.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780521196079i.jpg?v=1785805863","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/category-and-measure-infinite-combinatorics-topology-and-groups-hardback-9780521196079","provider":"Freshly Printed Books","version":"1.0","type":"link"}