{"product_id":"set-theory-paperback-softback-9781470464943","title":"Set Theory (Paperback \/ softback) 9781470464943","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSet Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eFelix Hausdorff (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781470464943\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 30 January 1957\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e352 pages\u003cbr\u003e23.3 x 15.4 x 2.2 cm, 0.492 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003eAn indispensible book for all those interested in the theory of sets and the allied branches of real variable theory.\"\" — \u003cem\u003eBulletin of the AMS\u003c\/em\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eIn the early twentieth century, Hausdorff developed an axiomatic approach to topology, which continues to be the foundation of modern topology. The present book, the English translation of the third edition of Hausdorff's \u003cem\u003eMengenlehre\u003c\/em\u003e, is a thorough introduction to his theory of point-set topology.\u003cbr\u003e\u003cbr\u003eThe treatment begins with topics in the foundations of mathematics, including the basics of abstract set theory, sums and products of sets, cardinal and ordinal numbers, and Hausdorff's well-ordering theorem. The exposition then specializes to point sets, where major topics such as Borel systems, first and second category, and connectedness are considered in detail. Next, mappings between spaces are introduced. This leads naturally to a discussion of topological spaces and continuous mappings between them. Finally, the theory is applied to the study of real functions and their properties.\u003cbr\u003e\u003cbr\u003eThe book does not presuppose any mathematical knowledge beyond calculus, but it does require a certain maturity in abstract reasoning; qualified college seniors and first-year graduate students should have no difficulty in making the material their own.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cul\u003e\n\u003cli\u003eSets and the Combining of Sets: 1.1 Sets\u003c\/li\u003e\n\u003cli\u003e 1.2 Functions\u003c\/li\u003e\n\u003cli\u003e 1.3 Sum and intersection\u003c\/li\u003e\n\u003cli\u003e 1.4 Product and power\u003c\/li\u003e\n\u003cli\u003e Cardinal Numbers: 2.5 Comparison of sets\u003c\/li\u003e\n\u003cli\u003e 2.6 Sum, product, and power\u003c\/li\u003e\n\u003cli\u003e 2.7 The scale of cardinal numbers\u003c\/li\u003e\n\u003cli\u003e 2.8 The elementary cardinal numbers\u003c\/li\u003e\n\u003cli\u003e Order Types: 3.9 Order\u003c\/li\u003e\n\u003cli\u003e 3.10 Sum and product\u003c\/li\u003e\n\u003cli\u003e 3.11 The types $\\aleph_0$ and $\\aleph$\u003c\/li\u003e\n\u003cli\u003e Ordinal Numbers: 4.12 The well-ordering theorem\u003c\/li\u003e\n\u003cli\u003e 4.13 The comparability of ordinal numbers\u003c\/li\u003e\n\u003cli\u003e 4.14 The combining of ordinal numbers\u003c\/li\u003e\n\u003cli\u003e 4.15 The alefs\u003c\/li\u003e\n\u003cli\u003e 4.16 The general concept of product\u003c\/li\u003e\n\u003cli\u003e Systems of Sets: 5.17 Rings and fields\u003c\/li\u003e\n\u003cli\u003e 5.18 Borel systems\u003c\/li\u003e\n\u003cli\u003e 5.19 Suslin sets\u003c\/li\u003e\n\u003cli\u003e Point Sets: 6.20 Distance\u003c\/li\u003e\n\u003cli\u003e 6.21 Convergence\u003c\/li\u003e\n\u003cli\u003e 6.22 Interior points and border points\u003c\/li\u003e\n\u003cli\u003e 6.23 The $\\alpha, \\beta$, and $\\gamma$ points\u003c\/li\u003e\n\u003cli\u003e 6.24 Relative and absolute concepts\u003c\/li\u003e\n\u003cli\u003e 6.25 Separable spaces\u003c\/li\u003e\n\u003cli\u003e 6.26 Complete spaces\u003c\/li\u003e\n\u003cli\u003e 6.27 Sets of the first and second categories\u003c\/li\u003e\n\u003cli\u003e 6.28 Spaces of sets\u003c\/li\u003e\n\u003cli\u003e 6.29 Connectedness\u003c\/li\u003e\n\u003cli\u003e Point Sets and Ordinal Numbers: 7.30 Hulls and kernels\u003c\/li\u003e\n\u003cli\u003e 7.31 Further applications of ordinal numbers\u003c\/li\u003e\n\u003cli\u003e 7.32 Borel and Suslin sets\u003c\/li\u003e\n\u003cli\u003e 7.33 Existence proofs\u003c\/li\u003e\n\u003cli\u003e 7.34 Criteria for Borel sets\u003c\/li\u003e\n\u003cli\u003e Mappings of Two Spaces: 8.35 Continuous mappings\u003c\/li\u003e\n\u003cli\u003e 8.36 Interval-images\u003c\/li\u003e\n\u003cli\u003e 8.37 Images of Suslin sets\u003c\/li\u003e\n\u003cli\u003e 8.38 Homeomorphism\u003c\/li\u003e\n\u003cli\u003e 8.39 Simple curves\u003c\/li\u003e\n\u003cli\u003e 8.40 Topological spaces\u003c\/li\u003e\n\u003cli\u003e Real Functions: 9.41 Functions and inverse image sets\u003c\/li\u003e\n\u003cli\u003e 9.42 Functions of the first class\u003c\/li\u003e\n\u003cli\u003e 9.43 Baire functions\u003c\/li\u003e\n\u003cli\u003e 9.44 Sets of convergence\u003c\/li\u003e\n\u003cli\u003e Supplement: 10.45 The Baire condition\u003c\/li\u003e\n\u003cli\u003e 10.46 Half-schlicht mappings\u003c\/li\u003e\n\u003cli\u003e Appendixes\u003c\/li\u003e\n\u003cli\u003e Bibliography\u003c\/li\u003e\n\u003cli\u003e Further references\u003c\/li\u003e\n\u003cli\u003e Index\u003c\/li\u003e\n\u003c\/ul\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003c\/font\u003e","brand":"American Mathematical Society","offers":[{"title":"Brand New","offer_id":52670852727064,"sku":"9781470464943","price":49.99,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/freshlyprintedbooks.co.uk\/products\/set-theory-paperback-softback-9781470464943","provider":"Freshly Printed Books","version":"1.0","type":"link"}