Continuous Selections of Multivalued Mappings

Continuous Selections of Multivalued Mappings

This book is the first systematic and comprehensive study of the theory of continuous selections of multivalued mappings. This interesting branch of modern topology was introduced by E.A. Michael in the 1950s and has since witnessed an intensive development with various applications outside topology, e.g. in geometry of Banach spaces, manifolds theory, convex sets, fixed points theory, differential inclusions, optimal control, approximation theory, and mathematical economics. The work can be used in different ways: the first part is an exposition of the basic theory, with details. The second part is a comprehensive survey of the main results. Lastly, the third part collects various kinds of applications of the theory. Audience: This volume will be of interest to graduate students and research mathematicians whose work involves general topology, convex sets and related geometric topics, functional analysis, global analysis, analysis on manifolds, manifolds and cell complexes, and mathematical economics.

---

Inhaltsangabe

Preface. A: Theory: 0. Preliminaries. 1.
Convex-Valued Selection Theorem. 2. Zero-Dimensional Selection
Theorem. 3. Relations between Zero-Dimensional and Convex-Valued
Selections. 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. Subject Index.

---

Inhaltsangabe

Preface. A: Theory: 0. Preliminaries. 1. Convex-Valued Selection Theorem. 2. Zero-Dimensional Selection Theorem. 3. Relations between Zero-Dimensional and Convex-Valued Selections. 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. Subject Index.