Open problems in topology
著者
書誌事項
Open problems in topology
North-Holland , Distributors for the U.S. and Canada, Elsevier Science Pub. Co., 1990-2007
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注記
Includes bibliographical references and indexes
2 edited by Elliott Pearl
2 published by Elsevier
内容説明・目次
- 巻冊次
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2 ISBN 9780444522085
内容説明
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.
目次
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 Lindeloef 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. 1/2-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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[1] ISBN 9780444887689
内容説明
FROM THE INTRODUCTION: "This volume grew from a discussion by the editors on the difficulty of finding good thesis problems for graduate students in topology. Although at any given time we each had our own favorite problems, we acknowledged the need to offer students a wider selection from which to choose a topic peculiar to their interests. One of us remarked, `Wouldn't it be nice to have a book of current unsolved problems always available to pull down from the shelf?' The other replied `Why don't we simply produce such a book?' Two years later and not so simply, here is the resulting volume. The intent is to provide not only a source book for thesis-level problems but also a challenge to the best researchers in the field."
目次
Set Theoretic Topology. Dow's Questions. Stepran's Problems. Tall's Problems. Problems I Wish I Could Solve. Weiss' Questions. Perfectly Normal Compacta, Cosmic Spaces, and Some Partition Problems. Open Problems on bv. On First Countable, Countably Compact Spaces III: The Problem of Obtaining Separable Noncompact Examples. Set-Theoretic Problems in Moore Spaces. Some Conjectures. Small Uncountable Cardinals and Topology. General Topology. A Survey of the Class MOBI. Problems on Perfect Ordered Spaces. The Point-Countable Base Problem. Some Open Problems in Densely Homogeneous Spaces. Large Homogeneous Compact Spaces. Some Problems. Questions in Dimension Theory. Continua Theory. Eleven Annotated Problems About Continua. Tree-Like Curves and Three Classical Problems. Topology and Algebraic Structures. Problems on Topological Groups and other Homogeneous Spaces. Problems in Domain Theory and Topology. Topology and Computer Science. Problems in the Topology of Binary Digital Images. On Relating Denotational and Operational Semantics for Programming Languages with Recursion and Concurrency. Algebraic and Geometric Topology. Problems on Topological Classification of Incomplete Metric Spaces. Problems about Finite-Dimensional Manifolds. A List of Open Problems in Shape Theory. Algebraic Topology. Problems in Knot Theory. Problems in Infinite-Dimensional Topology. Topology Arising from Analysis. Problems in C p -Theory. Problems in Topology Arising from Analysis. Dynamics. Continuum Theory and Topological Dynamics. One-Dimensional versus Two-Dimensional Dynamics. Index of General Terms. Index of Terms Used in the Problems.
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