Overview
- 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
Part of the book series: Problem Books in Mathematics (PBM)
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About this book
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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Table of contents (4 chapters)
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)
Authors and Affiliations
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.
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Bibliographic Information
Book Title: A Cp-Theory Problem Book
Book Subtitle: Functional Equivalencies
Authors: Vladimir V. Tkachuk
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-3-319-24385-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-24383-2Published: 14 April 2016
Softcover ISBN: 978-3-319-79616-1Published: 19 April 2018
eBook ISBN: 978-3-319-24385-6Published: 05 April 2016
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: XIV, 727
Topics: Topology
Keywords
- 1-equivalence
- Cp-theory
- Lindelof Sigma-property
- Lindelof space
- additional axioms of ZFC
- cardinal functions
- compact space
- convergence properties
- function spaces
- metrizability
- open questions topology
- pointwise convergence
- set t heory
- t-equivalence
- u-equivalence
- homeomorphisms of function spaces
- linear topological spaces
- l-equivalence
- continuous maps
- Cp-spaces