A Cp-Theory Problem Book: Functional Equivalencies

by Vladimir V. Tkachuk

Overview

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.

Product Details

ISBN-13:	9783319796161
Publisher:	Springer International Publishing
Publication date:	04/21/2018
Series:	Problem Books in Mathematics
Edition description:	Softcover reprint of the original 1st ed. 2016
Pages:	727
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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.

Table of Contents

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.

Editorial Reviews

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)

From the Publisher