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This volume of Vladimir Tkachuk´s series covers all the major topics in Cp-theory, providing 500 selected problems and exercises as well as their complete solutions and guiding the student from basic topological principles to the frontiers of modern research.

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This work is a continuation of the first volume published by Springer in 2011, entitled "A Cp-Theory Problem Book: Topological and Function Spaces." The first volume provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. This present volume covers a wide variety of topics in Cp-theory and general topology at the professional level bringing the reader to the frontiers of modern research. The volume contains 500 problems and exercises with complete solutions. It can also be used as an introduction to advanced set theory and descriptive set theory. The book presents diverse topics of the theory of function spaces with the topology of pointwise convergence, or Cp-theory which exists at the intersection of topological algebra, functional analysis and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from these areas of research. Moreover, this book gives a reasonably complete coverage of Cp-theory 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.

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Detailed Summary of Exercise Sections.- Preface.- Introduction.- 1. Duality Theorems and Properties of Function Spaces.- 2. Solutions of Problems 001-500.- 3. Bonus Results: Some Hidden statements.- 4. Open Problems.- Bibliography.- List of Special Symbols.- Index.

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"This is a well-written and very interesting book from several points of view and can be used as a textbook for courses in both C p -theory and general topology as well as a reference guide for specialists working in C p -theory and related topics. ... I hope that this book becomes the right hand of students and researchers in mathematics." (Dimitrios N. Georgiou, Mathematical Reviews, May, 2015)
"This volume, devoted to special properties of function spaces, is divided into four chapters ... . The concise beginning of each section contains definitions of topics used in that section. ... this problem book will become one of the table books for all researchers interested in C p -theory and its relations with other fields of mathematics." (Ljubisa D. Kocinac, zbMATH, Vol. 1303, 2015)

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