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Edited By Elliott Pearl, Toronto, Canada
Description 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.
Audience
Researchers and mathematicians
Contents
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. Hrusak 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. Hrusak and P. Simon)
20. Good, splendid and Jakovlev (I. Juhasz 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 Frechet
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 Lindelof 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. Martinez-de-la-Vega and J.M. Martinez-Montejano)
36. ?-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. Hernandez
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. Kunzi)
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
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