Continuous Selections of Multivalued Mappings - Theory

In this review of Continuous Selections of Multivalued Mappings the reviewer finds a deep, rigorous reference aimed at researchers and advanced students working with selection theory and its many applications. The single biggest reason to buy is its comprehensive treatment: the book collects foundational theorems, extended results and concrete uses across topology, functional analysis and game theory, making it a useful desk reference for anyone needing a compact source on continuous selection methods and their consequences.

Key Features

• Comprehensive theory: Part A lays out the core definitions and theorems that underpin continuous selection problems, helping readers build a clear conceptual foundation.
• Collected results: Part B gathers fundamental results and classical milestones, saving time for researchers who need a consolidated reference to historical and modern developments.
• Wide-ranging applications: Part C demonstrates applications in areas such as fixed-point theory, infinite-dimensional manifolds and mathematical economics, showing practical uses of abstract results.
• Historical perspective: The book traces the development of the field since E. Michael's foundational work in the 1950s, which aids understanding of why key approaches evolved.
• Modular structure: The three relatively independent parts let readers consult theory, results or applications separately according to immediate need.

Who It's For

This book is aimed primarily at graduate students, researchers and practitioners in topology, geometric topology, functional analysis and related fields who require a focused, rigorous account of continuous selections and multivalued mappings. The level and breadth make it a suitable companion for someone preparing to work on problems involving absolute retracts, fixed-point theorems, or economic models that use selection techniques.

It is less suitable for general readers or undergraduates without prior exposure to topology or functional analysis; those seeking an introductory textbook with exercises and pedagogical handholding should look for more elementary treatments before tackling this volume.

Pros & Cons

Pros

• Concise presentation of core theorems useful for reference and research.
• Clear linkage of theoretical results to applications across several branches of mathematics.
• Modular three-part organization lets readers target specific needs quickly.

Cons

• The book assumes significant background and is not an introductory textbook for novices.

Specifications

Our Verdict

Continuous Selections of Multivalued Mappings is a solid, value-packed reference for specialists who need a compact source of theory, consolidated results and concrete applications. Those with adequate background will find it a worthwhile investment for research and advanced study, while newcomers should complement it with more introductory texts.

Frequently Asked Questions

Does this book cover applications?
Yes. Part C collects applications in topology, fixed-point theory, manifolds, game theory and mathematical economics.

Is prior topology knowledge required?
Yes. The book presumes familiarity with general topology and functional analysis, so it is best for graduate-level readers and researchers.

How is the book organized?
It is organized in three relatively independent parts: theory, results and applications for targeted reading.