Hyperspaces: Fundamentals and Recent AdvancesCRC Press, 1999 M01 4 - 544 páginas Presents hyperspace fundamentals, offering a basic overview and a foundation for further study. Topics include the topology for hyperspaces, examples of geometric models for hyperspaces, 2x and C(X) for Peano continua X, arcs in hyperspaces, the shape and contractability of hyperspaces, hyperspaces and the fixed point property, and Whitney maps. The text contains examples and exercises throughout, and provides proofs for most results. |
Contenido
The Topology for Hyperspaces | 3 |
Geometric Models for Hyperspaces | 31 |
2X and CX for Peano Continua X | 75 |
IV | 97 |
A Brief Introduction to Whitney Maps | 105 |
Existence of an Order Arc from Ao to | 119 |
Kelleys Segments | 127 |
Spaces of Segments Sw | 134 |
Being an Arc | 245 |
Cone Hyperspace Property | 261 |
Whitney Levels | 305 |
Χ General Properties of Hyperspaces | 333 |
Dimension of CX | 347 |
Special Types of Maps between Hyperspaces | 363 |
More on Contractibility of Hyperspaces | 395 |
Products Cones and Hyperspaces | 413 |
Shape and Contractibility of Hyperspaces | 153 |
Hyperspaces and the Fixed Point Property | 181 |
Part | 205 |
140 | 229 |
Whitney Properties and WhitneyReversible | 231 |
Geometric Models | 471 |
Literature Related to Hyperspaces of Continua Since 1978 | 478 |
| 497 | |
Otras ediciones - Ver todas
Hyperspaces: Fundamentals and Recent Advances Alejandro Illanes,Sam Nadler Vista previa limitada - 2024 |
Términos y frases comunes
2x and C(X 2x or C(X A₁ absolute retract admissible Whitney map Amer arc-smooth arcwise connected assume chainable circle-like CL(X closed subset compact compactum component cone Cone(X connected continuum connectedness contains continuous function contractible Corollary defined Definition deformation retract denote a metric e-map Example Exercise exists F₁ F₁(X finite graph fixed point property following theorem Goodykoontz Hausdorff metric Hausdorff space Hence Hilbert cube Hint homeomorphism homotopy hyperspaces identity map Illanes indecomposable continuum induced map Lemma Let f level for C(X locally connected map for 2x Math metric space monotone nondegenerate nonempty open subset order arc Peano continuum positive Whitney level Proc prove pseudo-arc Question result S. B. Nadler Sb(A segment sequence sequential strong Whitney-reversible smooth dendroid strong Whitney-reversible property subcontinuum Theorem topological space Topology Appl triod Tymchatyn unicoherent W. J. Charatonik weakly confluent Whitney property Z-set