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.

Contains a wide variety of top-notch methods and results of Cp-theory and general topology presented with detailed proofs Presents and classifies 100 open problems in Cp-theory explaining their relationship with previous research Introduces the reader to the theories of u-equivalent spaces and l-equivalent spaces

Autorentext

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.

Klappentext

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.

Inhalt
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.