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Descriptive Topology in Selected Topics of Functional Analysis

  • Book
  • © 2011

Overview

Authors:
  1. Jerzy Kąkol

    1. , Faculty of Mathematics and Informatics, A. Mickiewicz University, Poznan, Poland

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  2. Wiesław Kubiś

    1. , Institute of Mathematics, Jan Kochanowski University, Kielce, Poland

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  3. Manuel López-Pellicer

    1. , IUMPA (Institute of Pure and Applied Mat, Universitat Poltècnica de València, València, Spain

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  • Presents numerous results that have previously only appeared in journal publications
  • Includes several newly developed and unpublished results
  • Can serve a supplementary text in course focusing on selected topics in functional analysis, set topology, or the theory or functional spaces
  • This is the first monograph to approach the topic of linear functional equations from the perspective of descriptive topology
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (20 chapters)

  1. Front Matter

    Pages I-XII
    Download chapter PDF

  2. Overview

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 1-11

  3. Elementary Facts about Baire and Baire-Type Spaces

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 13-62

  4. K-analytic and Quasi-Suslin Spaces

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 63-108

  5. Web-Compact Spaces and Angelic Theorems

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 109-135

  6. Strongly Web-Compact Spaces and a Closed Graph Theorem

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 137-142

  7. Weakly Analytic Spaces

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 143-181

  8. K-analytic Baire Spaces

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 183-191

  9. A Three-Space Property for Analytic Spaces

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 193-199

  10. K-analytic and Analytic Spaces C p (X)

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 201-237

  11. Precompact Sets in (LM)-Spaces and Dual Metric Spaces

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 239-242

  12. Metrizability of Compact Sets in the Class \(\mathfrak {G}\)

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 243-250

  13. Weakly Realcompact Locally Convex Spaces

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 251-278

  14. Corson’s Property (C) and Tightness

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 279-287

  15. Fréchet–Urysohn Spaces and Groups

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 289-303

  16. Sequential Properties in the Class \(\mathfrak{G}\)

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 305-326

  17. Tightness and Distinguished Fréchet Spaces

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 327-354

  18. Banach Spaces with Many Projections

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 355-394

  19. Spaces of Continuous Functions over Compact Lines

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 395-404

  20. Compact Spaces Generated by Retractions

    • Jerzy Kąkol, Wiesław Kubiś, Manuel López-Pellicer
    Pages 405-465
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Keywords

About this book

"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on 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 functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.

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)

Authors and Affiliations

  • , Faculty of Mathematics and Informatics, A. Mickiewicz University, Poznan, Poland

    Jerzy Kąkol

  • , Institute of Mathematics, Jan Kochanowski University, Kielce, Poland

    Wiesław Kubiś

  • , IUMPA (Institute of Pure and Applied Mat, Universitat Poltècnica de València, València, Spain

    Manuel López-Pellicer

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

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC 2011

  • Hardcover ISBN: 978-1-4614-0528-3Published: 30 August 2011

  • Softcover ISBN: 978-1-4614-3003-2Published: 24 October 2013

  • eBook ISBN: 978-1-4614-0529-0Published: 30 August 2011

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: XII, 496

  • Topics: Functional Analysis, Topology, Special Functions

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