Continuous Selections of Multivalued Mappings

D. Repovs, P.V. Semenov (Autoren)

Buch | Softcover

359 Seiten

2010 | 1st ed. Softcover of orig. ed. 1998
Springer (Verlag)
978-90-481-5111-0 (ISBN)

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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.

A. Theory.- §0. Preliminaries.- §1. Convex-valued selection theorem.- §2. Zero-dimensional selection theorem.- §3. Relations between Zero-dimensional and Convex-valued selection theorems.- §4. Compact-valued selection theorem.- §5. Finite-dimensional selection theorem.- §6. Examples and counterexamples.- §7. Addendum: New proof of Finite-dimensional selection theorem.- B. Results.- §1. Characterization of normality-type properties.- §2. Unified selection theorems.- §3. Selection theorems for non-lower semicontinuous mappings.- §4. Selection theorems for nonconvex-valued maps.- §5. Miscellaneous results.- §6. Measurable selections.- C. Applications.- §1. First applications.- §2. Regular mappings and locally trivial fibrations.- §3. Fixed-point theorems.- §4. Homeomorphism Group Problem.- §5. Soft mappings.- §6. Metric projections.- §7. Differential inclusions.- References.

Erscheint lt. Verlag	4.12.2010
Reihe/Serie	Mathematics and Its Applications ; 455
Zusatzinfo	VIII, 359 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	90-481-5111-2 / 9048151112
ISBN-13	978-90-481-5111-0 / 9789048151110
Zustand	Neuware