A Cp-Theory Problem Book: Functional Equivalencies (Problem Books in Mathematics)

Tkachuk, Vladimir V.

ISBN 10: 3319243837 / ISBN 13: 9783319243832

Editore: Springer, 2016

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Titolo: A Cp-Theory Problem Book: Functional ...

Casa editrice: Springer

Data di pubblicazione: 2016

Legatura: Rilegato

Condizione: New

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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.

Recensione:

“The book presents a systematic exposition of functional equivalences of Tychonoff spaces and provides many major results and methods in the area of C p -theory ... . intended for graduate and postgraduate students and for all those who are interested in learning more advanced results and investigation in this dynamic area of topology ... . a valuable reference source for several areas of general topology that can help to inform and direct future independent research.” (Ljubiša D. Kočinac, zbMATH 1354.54001, 2017)