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Mathematics - Analysis | Descriptive Topology in Selected Topics of Functional Analysis

Descriptive Topology in Selected Topics of Functional Analysis

Series: Developments in Mathematics, Vol. 24

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

2011, XII, 496 p.

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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  • Includes several newly developed and unpublished results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

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.

Content Level » Research

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

Related subjects » Analysis - Geometry & Topology

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