A Cp-Theory Problem Book

Functional Equivalencies

Vladimir V. Tkachuk (Autor)

Buch | Hardcover

XIV, 727 Seiten

2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-24383-2 (ISBN)

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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.

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.

Preface.-Detailed summary of exercise sections.-Introduction.-1. Properties Preserved by Homeomorphisms of Function Spaces.-2. Solutions of Problems 1-500.-3. Bonus Results: Some Hidden Statements.-4. Open Problems.-Bibliography.-List of Special Symbols.-Index.

"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." (Ljubisa D. Kocinac, zbMATH 1354.54001, 2017)

Erscheinungsdatum	15.02.2016
Reihe/Serie	Problem Books in Mathematics
Zusatzinfo	XIV, 727 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	1-equivalence • additional axioms of ZFC • Cardinal functions • Compact space • continuous maps • convergence properties • Cp-spaces • Cp-theory • function spaces • homeomorphisms of function spaces • l-equivalence • Lindelof Sigma-property • Lindelof space • linear topological spaces • mathematics and statistics • metrizability • open questions topology • pointwise convergence • set t heory • t-equivalence • Topology • u-equivalence
ISBN-10	3-319-24383-7 / 3319243837
ISBN-13	978-3-319-24383-2 / 9783319243832
Zustand	Neuware