Advertisement

© 2011

Descriptive Topology in Selected Topics of Functional Analysis

Book

Part of the Developments in Mathematics book series (DEVM, volume 24)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 1-11
  3. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 13-62
  4. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 63-108
  5. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 109-135
  6. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 137-142
  7. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 143-181
  8. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 183-191
  9. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 193-199
  10. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 201-237
  11. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 239-242
  12. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 243-250
  13. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 251-278
  14. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 279-287
  15. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 289-303
  16. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 305-326
  17. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 327-354
  18. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 355-394
  19. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 395-404
  20. Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 405-465

About this book

Introduction

A large mathematical community throughout the world actively works in functional analysis and uses profound techniques from topology. As the first monograph to approach the topic of topological vector spaces from the perspective of descriptive topology, this work provides also new insights into the connections between the topological properties of linear function spaces and their role in functional analysis. 

Descriptive Topology in Selected Topics of Functional Analysis is a self-contained volume that applies recent developments and classical results in descriptive topology to study the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, LF-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in distribution theory, differential equations, complex analysis, and various other areas of functional analysis.

Written by three experts in the field, this book is a treasure trove for researchers and graduate students studying the interplay among the areas of point-set and descriptive topology, modern analysis, set theory, topological vector spaces and Banach spaces, and continuous function spaces.  Moreover, it will serve as a reference for present and future work done in this area and could serve as a valuable supplement to advanced graduate courses in functional analysis, set-theoretic topology, or the theory of function spaces.

Keywords

Analysis C(X) Spaces Descriptive Enlargments Equations Function Spaces Functional Linear Spaces Set Topology

Authors and affiliations

  1. 1., Faculty of Mathematics and InformaticsA. Mickiewicz UniversityPoznanPoland
  2. 2., Institute of MathematicsJan Kochanowski UniversityKielcePoland
  3. 3., IUMPA (Institute of Pure and Applied MatUniversitat Poltècnica de ValènciaValènciaSpain

Bibliographic information

  • Book Title Descriptive Topology in Selected Topics of Functional Analysis
  • Authors Jerzy Kąkol
    Wiesław Kubiś
    Manuel López-Pellicer
  • Series Title Developments in Mathematics
  • DOI https://doi.org/10.1007/978-1-4614-0529-0
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4614-0528-3
  • Softcover ISBN 978-1-4614-3003-2
  • eBook ISBN 978-1-4614-0529-0
  • Series ISSN 1389-2177
  • Edition Number 1
  • Number of Pages XII, 496
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Functional Analysis
    Topology
    Special Functions
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

Reviews

From the reviews:

“The book summarizes many results which describe various aspects of the structure of topological vector spaces … . Most of the chosen material is relatively recent and appears in book form for the first time. … Together with a rich list of references the book can help in finding and understanding many finer questions concerning various aspects of the structure of subclasses of the class of topological vector spaces.” (Petr Holický, Zentralblatt MATH, Vol. 1231, 2012)

“The authors collect a large amount of material displaying connections between general topology and functional analysis with regard to properties of infinite-dimensional topological vector spaces. … It is a fine piece of scholarship with well-organized, readable proofs. … It is an encyclopedia of a subject meant for researchers and advanced graduate students likely interested in research for an advanced degree, and/or adding more knowledge to a course in which they are enrolled.” (E. Beckenstein, Mathematical Reviews, February, 2013)