Open Problems in Topology

Jan Van Mill, George M. Reed0444887687, 9780444887689

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.”

---

Table of contents :
Introduction……Page 3
Table of Contents……Page 5
Part I: Set Theoretic Topology……Page 13
Dow’s Questions……Page 15
Steprans’ Problems……Page 21
Tall’s Problems……Page 28
Problems I wish I could solve……Page 42
Weiss’s Questions……Page 81
Perfectly normal compacta, cosmic spaces, and some partition problems……Page 88
Open problems on ßw……Page 98
On first countable, countably compact spaces III: The problem of obtaining separable noncompact examples……Page 126
Set-theoretic problems in Moore spaces……Page 160
Some Conjectures……Page 178
Small uncountable cardinals and topology……Page 188
Part II: General Topology……Page 211
A Survey of the Class MOBI……Page 212
Problems in Perfect Ordered Spaces……Page 220
The Point-Countable Base Problem……Page 225
Some Open Problems in Densely Homogeneous Spaces……Page 238
Large Homogeneous Compact Spaces……Page 246
Some Problems……Page 255
Questions in Dimension Theory……Page 262
Part III: Continua Theory……Page 274
Eleven Annotated Problems About Continua……Page 275
Tree-like Curves and Three Classical Problems……Page 282
Part IV: Topology and Algebraic Structures……Page 289
Problems on Topological Groups and Other Homogeneous Spaces……Page 290
Problems in Domain Theory and Topology……Page 324
Part V: Topology and Computer Science……Page 347
Problems in the Topology of Binary Digital Images……Page 348
On Relating Denotational and Operational Semantics for Programming Languages with Recursion and Concurrency……Page 358
Part VI: Algebraic and Geometric Topology……Page 377
Problems on Topological Classiffcation of Incomplete Metric Spaces……Page 378
Problems about Finite-Dimensional Manifolds……Page 398
A List of Open Problems in Shape Theory……Page 422
Problems on Algebraic Topology……Page 432
Problems in Knot Theory……Page 449
Open Problems in Infinite Dimensional Topology……Page 484
Part VII: Topology Arising from Analysis……Page 558
Problems in Cp-theory……Page 559
Problems in Topology arising from Analysis……Page 573
Part VIII: Dynamics……Page 585
Continuum Theory and Topological Dynamics……Page 586
One-dimensional versus two-dimensional dynamics……Page 597
Index of general terms……Page 606
Index of terms used in the problems……Page 623