A Cp-theory problem book: functional equivalencies
by Tkachuk, V. V., (Vladimir Vladimirovich)
This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory℗ℓof functional equivalencies℗ℓthrough 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.℗ℓThe book presents complete and up-to-date information on the preservation of topological properties by homeomorphi…
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- Full title :A Cp-theory problem book : functional equivalencies / Vladimir V. Tkachuk.
Summary
This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory℗ℓof functional equivalencies℗ℓthrough 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.℗ℓThe book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. ℗ℓAn exhaustive theory of t-equivalent, ℗ℓu-equivalent and℗ℓl-equivalent spaces is developed from scratch. ℗ℓ The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as℗ℓ the theory of inverse systems and℗ℓdimension theory. Moreover, the inclusion of Kolmogorov's℗ℓsolution of Hilbert's Problem 13 is included as it is needed for℗ℓthe℗ℓpresentation of the theory of℗ℓl-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, ℗ℓ Gul'ko and Khmyleva's example of ℗ℓnon-preservation of℗ℓ compactness by t-equivalence, Okunev's method of constructing℗ℓ℗ℓl-equivalent spaces and the theorem of Marciszewski and Pelant on℗ℓu-invariance of absolute Borel sets. From the reviews of Special Features of Function Spaces: ℓ́ℓThis is a well-written and very interesting book from several points of view and can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists working in Cp-theory and related topics. Additionally, the material can also be considered as an introduction to advanced set theory and descriptive set theory. ℓ́ŒI hope that this book becomes the right hand of students and researchers in mathematics.ℓ́ℓ (Mathematical Reviews) From the reviews of Topological and Function Spaces: ℗ℓℓ́ℓIt is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research. The only background needed is some knowledge of set theory and real numbers. ℓ́ŒThis volume can also be used as a reference for mathematicians working in or outside of the field of topology (functional analysis) wanting to use results or methods of Cp-theory.ℓ́ℓ (Mathematical Reviews).
Read More ↓Edition Statements
- Publication Date:2016.
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham
- Language:eng
- Publication Date:2016.
The Physical Object
- Description:1 online resource (xiv, 727 pages)
Edition Identifiers
- ISBN:9783319243856, 3319243853, 3319243837, 9783319243832, 9783319243849, 3319243845, 9783319796161, 331979616X
- DOI:10.1007/978-3-319-24385-6
- oclc:ocn946315754
- LC Classification:QA323
- Dewey Decimal:515/.73
Table of Contents
Intro; Preface; Contents; Detailed Summary of Exercises; 1.1. Equivalencies That Arise From Homeomorphisms of Cp(X).; 1.2. Uniformities, Dimension, and u-Equivalence.; 1.3. Linear Topological Spaces and l-Equivalence.; 1.4. Metrizable Spaces and l-Equivalence.; 1.5. The Last-Minute Updates. Yet More on l-Equivalence.; Introduction; 1 Properties Preserved by Homeomorphismsof Function Spaces; 1.1 Equivalences that arise from homeomorphisms of Cp(X); 1.2 Uniformities, Dimension, and u-Equivalence; 1.3 Linear Topological Spaces and l-Equivalence; 1.4 Metrizable Spaces and l-Equivalence
1.5 The Last-Minute Updates. Yet More on l-Equivalence1.6 Bibliographic notes to Chapter 1; 2 Solutions of problems 001-500; 3 Bonus results: Some Hidden Statements; 3.1 Standard spaces; 3.2 Compact spaces and their generalizations; 3.3 Properties of continuous maps; 3.4 Cardinal invariants and set theory; 3.5 Locally Convex Spaces and Homotopies; 3.6 Zero-dimensional Spaces and Connected Spaces; 3.7 Raznoie (Unclassified results); 4 Open problems; 4.1 Mappings which involve Cp-spaces; 4.2 Properties preserved by t-equivalence; 4.3 Properties preserved by u-equivalence
4.4 Properties preserved by l-eq…
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