Developments in Mathematics

Descriptive Topology in Selected Topics of Functional Analysis

Authors: Kąkol, Jerzy, Kubiś, Wiesław, López-Pellicer, Manuel

  • 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  • Includes several newly developed and unpublished results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
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eBook $179.00
price for USA (gross)
  • ISBN 978-1-4614-0529-0
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  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $229.00
price for USA
  • ISBN 978-1-4614-0528-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $229.00
price for USA
  • ISBN 978-1-4614-3003-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
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About this book

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.

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)


Table of contents (20 chapters)

  • Overview

    Kąkol, Jerzy (et al.)

    Pages 1-11

  • Elementary Facts about Baire and Baire-Type Spaces

    Kąkol, Jerzy (et al.)

    Pages 13-62

  • K-analytic and Quasi-Suslin Spaces

    Kąkol, Jerzy (et al.)

    Pages 63-108

  • Web-Compact Spaces and Angelic Theorems

    Kąkol, Jerzy (et al.)

    Pages 109-135

  • Strongly Web-Compact Spaces and a Closed Graph Theorem

    Kąkol, Jerzy (et al.)

    Pages 137-142

Buy this book

eBook $179.00
price for USA (gross)
  • ISBN 978-1-4614-0529-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $229.00
price for USA
  • ISBN 978-1-4614-0528-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $229.00
price for USA
  • ISBN 978-1-4614-3003-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Descriptive Topology in Selected Topics of Functional Analysis
Authors
Series Title
Developments in Mathematics
Series Volume
24
Copyright
2011
Publisher
Springer US
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4614-0529-0
DOI
10.1007/978-1-4614-0529-0
Hardcover ISBN
978-1-4614-0528-3
Softcover ISBN
978-1-4614-3003-2
Series ISSN
1389-2177
Edition Number
1
Number of Pages
XII, 496
Topics