Celebrating the work of world-renowned mathematician Sam B. Nadler, Jr., this reference examines the most recent advances in the analysis of continua. The book offers articles on the contributions of Professor Nadler, theorems on the structure and uniqueness of hyperspaces, results on the dynamics of solenoids, examples involving inverse limits of maps of the interval conditions on embeddability of hyperspaces and symmetric products, open problems on a number of topics. It examines boundary bumping theorems, fixed point theorems for nonseparating plane continua, Whitney maps and Whitney properties, topological entropy for arc-like continua, a variety of mapping properties, and more.
Table of Contents
Introduction 1. The Life and Times of Sam B. Nadler, Jr. 2. The Work of Sam B. Nadler, Jr. on Hyperspaces 3. Continua with Unique Hyperspace 4. Ordered Embeddings of Hyperspaces 5. Embedding Symmetric Products in Euclidean Spaces 6. On Strongly Monotone Mappings 7. On Semi-Universal Mappings 8. Problems on Hyperspace Retractions 9. The Dynamics of Maps of Solenoids Homotopic to the Identity 10. The Buckethandle Continuum Admits No Mean 11. Inverse Limits on [0,1] Using Piecewise Linear Unimodal Bonding Maps, II 12. A Tale of Six Atriodic Tree-Like Continua 13. Hyperspaces Locally 2-Cell at the Top 14. Cantor Sets of Ray Composants in Local Siegel Disk Boundaries 15. The RNT Property of Compactifications of the Ray 16. Non-Confluence of the Natural Map of Products onto Symmetric Products 17. Boundary Bumping in Connected Topological Spaces 18. The Selection Space of a Dendroid, I 19. On Period Three and Topological Entropy in Hereditarily Decomposable Arc-Like Continua 20. A Fixed Point Theorem for Certain Maps on Certain Nonseparating Plane Continua 21. Dendroids, Digraphs, and Posets 22. Sequential Decreasing Whitney Properties 23. More on Products of Effros Spaces 24. Continua Irreducible About n Points 25. A Note on Computation of Span 26. Spans of Spaces Contained in a Convex Disc Cross an Arc
Illanes\, Alejandro; Macias\, Sergio; Lewis\, Ira