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Continuous Selections of Multivalued Mappings

  • Book
  • © 1998

Overview

Authors:
  1. Dušan Repovš

    1. Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia

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  2. Pavel Vladimirovič Semenov

    1. Department of Mathematics, Moscow City Pedagogical University, Moscow, Russia

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 455)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-3
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  2. Theory

    1. Preliminaries

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 5-32

    2. Convex-Valued Selection Theorem

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 33-53

    3. Zero-Dimensional Selection Theorem

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 54-59

    4. Relations Between Zero-Dimensional and Convex-Valued Selection Theorems

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 60-74

    5. Compact-Valued Selection Theorem

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 75-83

    6. Finite-Dimensional Selection Theorem

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 84-114

    7. Examples and Counterexamples

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 115-125

    8. Addendum: New Proof of Finite-Dimensional Selection Theorem

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 126-145

  3. Results

    1. Characterization of Normality-Type Properties

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 146-154

    2. Unified Selection Theorems

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 155-159

    3. Selection Theorems for Non-Lower Semicontinuous Mappings

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 160-172

    4. Selection Theorems for Nonconvex-Valued Maps

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 173-185

    5. Miscellaneous Results

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 186-214

    6. Measurable Selections

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 215-231

  4. Applications

    1. First Applications

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 232-246

    2. Regular Mappings and Locally Trivial Fibrations

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 247-260

    3. Fixed-Point Theorems

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 261-273

    4. Homeomorphism Group Problem

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 274-280

    5. Soft Mappings

      • Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 281-299
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Keywords

About this book

This book is dedicated to the theory of continuous selections of multi­ valued mappings, a classical area of mathematics (as far as the formulation of its fundamental problems and methods of solutions are concerned) as well as !'J-n area which has been intensively developing in recent decades and has found various applications in general topology, theory of absolute retracts and infinite-dimensional manifolds, geometric topology, fixed-point theory, functional and convex analysis, game theory, mathematical economics, and other branches of modern mathematics. The fundamental results in this the­ ory were laid down in the mid 1950's by E. Michael. The book consists of (relatively independent) three parts - Part A: Theory, Part B: Results, and Part C: Applications. (We shall refer to these parts simply by their names). The target audience for the first part are students of mathematics (in their senior year or in their first year of graduate school) who wish to get familiar with the foundations of this theory. The goal of the second part is to give a comprehensive survey of the existing results on continuous selections of multivalued mappings. It is intended for specialists in this area as well as for those who have mastered the material of the first part of the book. In the third part we present important examples of applications of continuous selections. We have chosen examples which are sufficiently interesting and have played in some sense key role in the corresponding areas of mathematics.

Authors and Affiliations

  • Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia

    Dušan Repovš

  • Department of Mathematics, Moscow City Pedagogical University, Moscow, Russia

    Pavel Vladimirovič Semenov

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