Open Problems in Topology II

ISBN-13: 9780444522085 / Angielski / Twarda / 2007 / 763 str.

Elliott M. Pearl

Opis

This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis.

* New surveys of research problems in topology
* New perspectives on classic problems
* Representative surveys of research groups from all around the world

Spis treści

Part 1. General Topology

1. Selected ordered space problems (H. Bennett and D. Lutzer)
2. Problems on star-covering properties (M. Bonanzinga and M. Matveev)
3. Function space topologies (D.N. Georgiou, S.D. Iliadis and F. Mynard)
4. Spaces and mappings: special networks (C. Liu and Y. Tanaka)
5. Extension problems of real-valued continuous functions (H. Ohta and K. Yamazaki)
6. LE(k)-spaces (O. Okunev)
7. Problems on (ir) resolvability (O. Pavlov)
8. Topological games and Ramsey theory (M. Scheepers)
9. Selection principles and special sets of reals (B. Tsaban)

Part 2. Set-theoretic Topology

10. Introduction: Twenty problems in set-theoretic topology (M. Hrusák and J.T. Moore)
11. Thin-tall spaces and cardinal sequences (J. Bagaria)
12. Sequential order (A. Dow)
13. On D-spaces (T. Eisworth)
14. The fourth head of BN (I. Farah)
15. Are stratifiable spaces M1? (G. Gruenhage)
16. Perfect compacta and basis problems in topology (G. Gruenhage and J.T. Moore)
17. Selection problems for hyperspaces (V. Gutev and T. Nogura)
18. Efimov's problem (K.P. Hart)
19. Completely separable MAD families (M. Hrusák and P. Simon)
20. Good, splendid and Jakovlev (I. Juhász and W.A.R. Weiss)
21. Homogeneous compacta (J. van Mill)
22. Compact spaces with hereditarily normal squares (J.T. Moore)
23. The metrization problem for Fréchet groups (J.T. Moore and S. Todorcevic)
24. Cech-Stone remainders of discrete spaces (P.J. Nyikos)
25. First countable, countably compact, noncompact spaces (P.J. Nyikos)
26. Linearly Lindelöf problems (E. Pearl)
27. Small Dowker spaces (P.J. Szeptycki)
28. Reflection of topological properties to N1 (F.D. Tall)
29. The Scarborough-Stone problem (J.E. Vaughan)

Part 3. Continuum Theory

30. Questions in and out of context (D.P. Bellamy)
31. An update on the elusive fixed-point property (C.L. Hagopian)
32. Hyperspaces of continua (A. Ilanes)
33. Inverse limits and dynamical systems (W.T. Ingram)
34. Indecomposable continua (W. Lewis)
35. Open problems on dendroids (V. Martínez-de-la-Vega and J.M. Martínez-Montejano)
36. ½-Homogeneous continua (S.B. Nadler, Jr.)
37. Thirty open problems in the theory of homogeneous continua (J.R. Prajs)

Part 4. Topological Algebra

38. Problems about the uniform structures of topological groups (A. Bouziad and J-P. Troallic)
39. On some special classes of continuous maps (M.M. Clementino and D. Hofmann)
40. Dense subgroups of compact groups (W.W. Comfort)
41. Selected topics from the structure theory of topological groups (D. Dikranjan and D. Shakhmatov)
42. Recent results and open questions relating Chu duality and Bohr compactifications of locally compact groups (J. Galindo, S. Hernández and T-S. Wu)
43. Topological transformation groups: selected topics (M. Megrelishvili)
44. Forty-plus annotated questions about large topological groups (V. Pestov)

Part 5. Dynamical Systems

45. Minimal flows (W.F. Basener, K. Parwani and T. Wiandt)
46. The dynamics of tiling spaces (A. Clark)
47. Open problems in complex dynamics and "complex" topology (R.L. Devaney)
48. The topology and dynamics of flows (M.C. Sullivan)

Part 6. Computer Science

49. Computational topology (D. Blackmore and T.J. Peters)

Part 7. Functional Analysis

50. Non-smooth analysis, optimisation theory and Banach space theory (J.M. Borwein and W.B. Moors)
51. Topological structures of ordinary differential equations (V.V. Filippov)
52. The interplay between compact spaces and the Banach spaces of their continuous functions (P. Koszmider)
53. Tightness and t-equivalence (O. Okunev)
54. Topological problems in nonlinear and functional analysis (B. Ricceri)
55. Twenty questions on metacompactness in function spaces (V.V. Tkachuk)

Part 8. Dimension Theory

56. Open problems in infinite-dimensional topology (T. Banakh, R. Cauty and M. Zarichnyi)
57. Classical dimension theory (V.A. Chatyrko)
58. Questions on weakly infinite-dimensional spaces (V.V. Fedorchuk)
59. Some problems in the dimension theory of compacta (B.A. Pasynkov)

Part 9. Invited Papers

60. Problems from the Lviv topological seminar (T. Banakh, B. Bokalo, I. Guran, T. Radul and M. Zarichnyi)
61. Problems from the Bizerte-Sfax-Tunis Seminar (O. Echi, H. Marzougui and E. Salhi)
62. Cantor set problems (D.J. Garity and D. Repovs)
63. Problems from the Galway Topology Colloquium (C. Good, A. Marsh, A. McCluskey and B. McMaster)
64. The lattice of quasi-uniformities (E.P. de Jager amd H-P.A. Künzi)
65. Topology in North Bay: some problems in continuum theory, dimension theory and selections (A. Karasev, M. Tuncali and V. Valov)
66. Moscow questions on topological algebra (K.L. Kozlov, E.A. Reznichenko and O.V. Sipacheva)
67. Some problems from George Mason University (J. Kulesza, R. Levy and M. Matveev)
68. Some problems on generalized metrizable spaces (S. Lin)
69. Problems from the Madrid Department of Geometry and Topology (J.M.R. Sanjurjo)
70. Cardinal sequences and universal spaces (L. Soukup)

List of contributors
Index