位相幾何学の未解決問題2<br>Open Problems in Topology II

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位相幾何学の未解決問題2
Open Problems in Topology II

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  • 製本 Hardcover:ハードカバー版/ページ数 763 p.
  • 言語 ENG
  • 商品コード 9780444522085
  • DDC分類 514

基本説明

A collection of surveys of research problems in General Topology and its related fields of Mathematics.

Full 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.

Table of Contents

Part 1. General Topology                           1
Chapter 1. Selected ordered space problems 3
Harold Bennett and David Lutzer
Chapter 2. Problems on star-covering 9
properties
Maddalena Bonanzinga and Mikhail Matveev
Chapter 3. Function space topologies 15
Dimitris N. Georgiou, Stavros D. Iliadis
and Fr馘駻ic Mynard
Chapter 4. Spaces and mappings: special 23
networks
Chuan Liu and Yoshio Tanaka
Chapter 5. Extension problems of real-valued 35
continuous functions
Haruto Ohta and Kaori Yamazaki
Chapter 6. LΣ(kappa)-spaces 47
Oleg Okunev
Chapter 7. Problems on (ir)resolvability 51
Oleg Pavlov
Chapter 8. Topological games and Ramsey 61
theory
Marion Scheepers
Chapter 9. Selection principles and special 91
sets of Teals
Boaz Tsaban
Part 2. Set-theoretic Topology 109
Chapter 10. Introduction: Twenty problems in 111
set-theoretic topology
Michael Hru啾k and Justin Tatch Moore
Chapter 11. Thin-tall spaces and cardinal 115
sequences
Joan Bagaria
Chapter 12. Sequential order 125
Alan Dow
Chapter 13. On D-spaces 129
Todd Eisworth
Chapter 14. The fourth head of βN 135
Ilijas Farah
Chapter 15. Arc stratifiable spaces M1? 143
Gary Gruenhage
Chapter 16. Perfect compacta and basis 151
problems in topology
Gary Gruenhage and Justin Tatch Moore
Chapter 17. Selection problems for hyperspaces 161
Valentin Gutev and Tsugunori Nogura
Chapter 18. Efimov's problem 171
Klaas Pieter Hart
Chapter 19. Completely separable MAD families 179
Michael Hrukik and Petr Simon
Chapter 20. Good, splendid and Jakovlev 185
Istvan Juhasz and William A.R. Weiss
Chapter 21. Homogeneous compacta 189
Jan van Mill
Chapter 22. Compact spaces with hereditarily 197
normal squares
Justin Tatch Moore
Chapter 23. The metrization problem for 201
Fr馗het groups
Justin Tatch Moore and Stevo Todorcevic
Chapter 24. Cech亡tone remainders of discrete 207
spaces
Peter J. Nyikos
Chapter 25. First countable, countably 217
compact, noncompact spaces
Peter J. Nyikos
Chapter 26. Linearly Lindekif problems 225
Elliott Pearl
Chapter 27. Small Dowker spaces 233
Paul J. Szeptycki
Chapter 28. Reflection of topological 241
properties to N1
Franklin D. Tall
Chapter 29. The Scarborough- Stone problem 249
Jerry E. Vaughan
Part 3. Continuum Theory 257
Chapter 30. Questions in and out of context 259
David P. Bellamy
Chapter 31. An update on the elusive 263
fixed-point property
Charles L. Hagopian
Chapter 32. Hyperspaces of continua 279
Alejandro Manes
Chapter 33. Inverse limits and dynamical 289
systems
W.T. Ingram
Chapter 34. Indecomposable continua 303
Wayne Lewis
Chapter 35. Open problems on dendroids 319
Veronica Martinez-de-la-Vega and Jorge M.
Martinez-Montejano
Chapter 36. ス-Homogeneous continua 335
Sam B. Nadler, Jr.
Chapter 37. Thirty open problems in the 345
theory of homogeneous continua
Janusz R. Prajs
Part 4. Topological Algebra 357
Chapter 38. Problems about the uniform 359
structures of topological groups
Ahmed Bouziad and Jean-Pierre Troallic
Chapter 39. On some special classes of 367
continuous maps
Maria Manuel Clementino and Dirk Hofmann
Chapter 40. Dense subgroups of compact groups 377
W.W. Comfort
Chapter 41. Selected topics from the 389
structure theory of topological groups
Dikran Dikranjan and Dmitri Shakhmatov
Chapter 42. Recent results and open questions 407
relating Chu duality and Bohr
compactifications of locally compact groups
Jorge Galindo, Salvador Hernandez and
Ta-Sun Wu
Chapter 43. Topological transformation 423
groups: selected topics
Michael Megrelishvili
Chapter 44. Forty-plus annotated questions 439
about large topological groups
Vladimir Pestov
Part 5. Dynamical Systems 451
Chapter 45. Minimal flows 453
William F. Basener, Kamlesh Parwani and
Tamas Wiandt
Chapter 46. The dynamics of tiling spaces 463
Alex Clark
Chapter 47. Open problems in complex dynamics 469
and "complex.' topology
Robert L. Devaney
Chapter 48. The topology and dynamics of flows 479
Michael C. Sullivan
Part 6. Computer Science 491
Chapter 49. Computational topology 493
Denis Blackmore and Thomas J. Peters
Part 7. Functional Analysis 547
Chapter 50. Non-smooth analysis, optimisation 549
theory and Banach space theory
Jonathan M. Borwein and Warren B. Moors
Chapter 51. Topological structures of 561
ordinary differential equations
V.V. Filippov
Chapter 52. The interplay between compact 567
spaces and the Banach spaces of their
continuous functions
Piotr Koszmider
Chapter 53. Tightness and t-equivalence 581
Oleg Okunev
Chapter 54. Topological problems in nonlinear 585
and functional analysis
Biagio Ricceri
Chapter 55. Twenty questions on 595
metacompactness in function spaces
V.V. Tkactnik
Part 8. Dimension Theory 599
Chapter 56. Open probleins in 601
infinite-dimensional topology
Taras Banakh, Robert Canty amid Michael
Zarichnyi
Chapter 57. Classical dimension theory 625
Vitalij A. Chatyrko
Chapter 58. Questions oil weakly 637
infinite-dimensional spaces
Vitalii V. Fedorehuk
Chapter 59. Some problems in the dimension 647
theory of compacta
Boris A. Pasynkov
Part 9. Invited Problems 653
Chapter 60. Problems from the Lviv 655
topological seminar
Taras Banakh, Bohdan Bokalo, Igor Guran,
Taras Radul, Michael Zarichnvi
Chapter 61. Problems from the 669
Bizerte亡fax傍unis Seminar
Othman Echi, Habib Marzougui and Ezeddine
Salhi
Chapter 62. Cantor set problems 675
Dennis J. Garity and Dusan Repov 
Chapter 63. Problems from the Galway Topology 679

Colloquium

Chris Good, Andrew Marsh, Aisling McCluskey

and Brian McMaster

Chapter 64. The lattice of quasi-uniformities 691

Eliza P. de Jager and Hans-Peter A. K zi

Chapter 65. Topology in North Bay: some 697

problems in continuum theory, dimension

theory and selections

Alexandre Karasev, Murat Tuncali and Vesko

Valov

Chapter 66. Moscow questions on topological 711

algebra

Konstantin L. Kozlov, Evgenii A.

Reznichenko and Ol'ga V. Sipacheva

Chapter 67. Some problems from George Mason 727

University

John Kulesza, Ronnie Levy and Mikhail

Matveev

Chapter 68. Some problems on generalized 731

metrizable spaces

Shou Lin

Chapter 69. Problems from the Madrid 737

Department of Geometry and Topology

Jos M.R. Sanjurjo

Chapter 70. Cardinal sequences and universal 743

spaces

Lajos Soukup

List of contributors 747

Index 751