Vladimir V. Tkachuk's Books

A Cp-Theory Problem Book

Compactness in Function Spaces

By: Vladimir V. Tkachuk

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A Cp-Theory Problem Book

Compactness in Function Spaces

By: Vladimir V. Tkachuk

This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level. The first volume, Topological and Function Spaces © 2011, 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. The second volume, Special Features of Function Spaces © 2014, continued from the first, giving reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. This third volume is self-contained and works in tandem with the other two, containing five hundred carefully selected problems and solutions. It can also be considered as an introduction to advanced set theory and descriptive set theory, presenting diverse topics of the theory of function spaces with the topology of point wise convergence, or Cp-theory which exists at the intersection of topological algebra, functional analysis and general topology.

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Page Count

538

Publisher

Springer

Published Date

ISBN 10

3319160923

ISBN 13

9783319160924

A Cp-Theory Problem Book

Functional Equivalencies

By: Vladimir V. Tkachuk

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A Cp-Theory Problem Book

Functional Equivalencies

By: Vladimir V. Tkachuk

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.

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Page Count

740

Publisher

Springer

Published Date

ISBN 10

3319243853

ISBN 13

9783319243856

A Cp-Theory Problem Book

Compactness in Function Spaces

By: Vladimir V. Tkachuk

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A Cp-Theory Problem Book

Compactness in Function Spaces

By: Vladimir V. Tkachuk

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Solve jigsaw puzzle

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Page Count

538

Publisher

Springer

Published Date

ISBN 10

3319160923

ISBN 13

9783319160924

A Cp-Theory Problem Book

Special Features of Function Spaces

By: Vladimir V. Tkachuk

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A Cp-Theory Problem Book

Special Features of Function Spaces

By: Vladimir V. Tkachuk

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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Page Count

595

Publisher

Springer

Published Date

ISBN 10

3319047477

ISBN 13

9783319047478

Book's by Vladimir V. Tkachuk

A Cp-Theory Problem Book

A Cp-Theory Problem Book

A Cp-Theory Problem Book

A Cp-Theory Problem Book

A Cp-Theory Problem Book

A Cp-Theory Problem Book

A Cp-Theory Problem Book

A Cp-Theory Problem Book

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