A Cp-Theory Problem Book : Functional Equivalencies

Vladimir V. Tkachuk

ISBN 10: 3319243837 / ISBN 13: 9783319243832

Editore: Palgrave Macmillan, 2016

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nach der Bestellung gedruckt Neuware - Printed after ordering - This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theoryof functional equivalenciesthrough 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-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 t-equivalent,u-equivalent andl-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 anddimension theory. Moreover, the inclusion of Kolmogorov'ssolution of Hilbert's Problem 13 is included as it is needed forthepresentation of the theory ofl-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 t-equivalence, Okunev's method of constructingl-equivalent spaces and the theorem of Marciszewski and Pelant onu-invariance of absolute Borel sets.

Codice articolo 9783319243832

Dati bibliografici

• Titolo: A Cp-Theory Problem Book : Functional Equivalencies
• Editore: Palgrave Macmillan
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 3319243837
• ISBN 13: 9783319243832
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 46 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 46 millimetri di profondità
• Peso: 1267 grammi

Descrizione articolo

Riassunto

This fourth volume in Vladimir Tkachuk's series on Cp-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 Cp-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 t-equivalent, u-equivalent and l-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 l-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 t-equivalence, Okunev's method of constructing  l-equivalent spaces and the theorem of Marciszewski and Pelant on u-invariance of absolute Borel sets.

Informazioni sull'autore

Vladimir 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 A Cp-Theory Problem Book: Compactness in Function Spaces (Springer, 2015), A Cp-Theory Problem Book: Special Features of Function Spaces (Springer, 2014) and A Cp-Theory Problem Book: Topological and Function Spaces (Springer, 2011). All volumes have published in the Problem Books in Mathematics series.