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Continuous Selections of Multivalued Mappings

  • Dušan Repovš
  • Pavel Vladimirovič Semenov

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

Table of contents

  1. Front Matter
    Pages i-3
  2. Theory

    1. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 5-32
    2. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 33-53
    3. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 54-59
    4. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 60-74
    5. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 75-83
    6. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 84-114
    7. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 115-125
    8. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 126-145
  3. Results

    1. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 146-154
    2. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 155-159
    3. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 160-172
    4. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 173-185
    5. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 186-214
    6. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 215-231
  4. Applications

    1. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 232-246
    2. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 247-260
    3. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 261-273
    4. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 274-280
    5. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 281-299
    6. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 300-310
    7. Dušan Repovš, Pavel Vladimirovič Semenov
      Pages 311-329
  5. Back Matter
    Pages 330-359

About this book

Introduction

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.

Keywords

Dimension Grad Homeomorphism functional analysis manifold topology

Authors and affiliations

  • Dušan Repovš
    • 1
  • Pavel Vladimirovič Semenov
    • 2
  1. 1.Department of MathematicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Department of MathematicsMoscow City Pedagogical UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-1162-3
  • Copyright Information Springer Science+Business Media B.V. 1998
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5111-0
  • Online ISBN 978-94-017-1162-3
  • Buy this book on publisher's site