{"product_id":"a-cp-theory-problem-book-functional-equivalencies-hardcover","title":"A Cp-Theory Problem Book: Functional Equivalencies - 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\u003eVladimir V. Tkachuk\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eThis fourth volume in Vladimir Tkachuk's series on \u003ci\u003eCp\u003c\/i\u003e-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of \u003ci\u003eCp\u003c\/i\u003e-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of \u003ci\u003et\u003c\/i\u003e-equivalent, \u003ci\u003eu\u003c\/i\u003e-equivalent and \u003ci\u003el\u003c\/i\u003e-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of \u003ci\u003el\u003c\/i\u003e-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of compactness by \u003ci\u003et\u003c\/i\u003e-equivalence, Okunev's method of constructing \u003ci\u003el\u003c\/i\u003e-equivalent spaces and the theorem of Marciszewski and Pelant on \u003ci\u003eu\u003c\/i\u003e-invariance of absolute Borel sets.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003eThis fourth volume in Vladimir Tkachuk's series on \u003ci\u003eCp\u003c\/i\u003e-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of \u003ci\u003eCp\u003c\/i\u003e-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of \u003ci\u003et\u003c\/i\u003e-equivalent, \u003ci\u003eu\u003c\/i\u003e-equivalent and \u003ci\u003el\u003c\/i\u003e-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of \u003ci\u003el\u003c\/i\u003e-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of compactness by \u003ci\u003et\u003c\/i\u003e-equivalence, Okunev's method of constructing \u003ci\u003el\u003c\/i\u003e-equivalent spaces and the theorem of Marciszewski and Pelant on \u003ci\u003eu\u003c\/i\u003e-invariance of absolute Borel sets.\u003cbr\u003eFrom the reviews of \u003ci\u003eSpecial Features of Function Spaces\u003c\/i\u003e: \"This is a well-written and very interesting book from several points of view and can be used as a textbook for courses in both \u003ci\u003eCp\u003c\/i\u003e-theory and general topology as well as a reference guide for specialists working in \u003ci\u003eCp\u003c\/i\u003e-theory and related topics. Additionally, the material can also be considered as an introduction to advanced set theory and descriptive set theory. ...I hope that this book becomes the right hand of students and researchers in mathematics.\" (\u003cb\u003eMathematical Reviews\u003c\/b\u003e)\u003cp\u003e\u003c\/p\u003e \u003cp\u003eFrom the reviews of \u003ci\u003eTopological and Function Spaces\u003c\/i\u003e: \"It is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research. The only background needed is some knowledge of set theory and real numbers. ...This volume can also be used as a reference for mathematicians working in or outside of the field of topology (functional analysis) wanting to use results or methods of Cp-theory.\" (\u003cb\u003eMathematical Reviews\u003c\/b\u003e)\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003eVladimir V. Tkachuk is a professor in the Department of Mathematics of the Autonomous Metropolitan University in Mexico City. He holds a PhD from Moscow State University and is the author of\u003ci\u003e A Cp-Theory Problem Book: Compactness in Function Spaces \u003c\/i\u003e(Springer, 2015)\u003ci\u003e, \u003c\/i\u003e\u003ci\u003eA Cp-Theory Problem Book: Special Features of Function Spaces\u003c\/i\u003e (Springer, 2014) and \u003ci\u003eA Cp-Theory Problem Book: Topological and Function Spaces\u003c\/i\u003e (Springer, 2011). All volumes have published in the Problem Books in Mathematics series.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 727\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.56 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e April 14, 2016\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47337007317241,"sku":"9783319243832","price":137.68,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/UXVheXhWMWU5enNieVJlY1d5ODMxZz09.webp?v=1769674538","url":"https:\/\/bookscloud.io\/products\/a-cp-theory-problem-book-functional-equivalencies-hardcover","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}