Matches for: Author/Related=van Mill and Reed

Matches for: Author/Related=van Mill and Reed	MSN-Support	Help

0 items in clipboard; (500 item maximum; items will be lost after 2 hours of MathSciNet inactivity)

92c:54001 54-06 (55-06)
Open problems in topology.
Edited by Jan van Mill and George M. Reed.
North-Holland Publishing Co., Amsterdam, 1990. xiv+692 pp. \$92.25. ISBN 0-444-88768-7

References: 0

Reference Citations: 0

Review Citations: 80

Contents: Alan Dow, Dow's questions (pp. 5--11); Juris Steprans, Steprans' problems (pp. 13--20); F. D. Tall, Tall's problems (pp. 21--35); Stephen Watson [W. Stephen Watson], Problems I wish I could solve (pp. 37--76); William Weiss, Weiss's questions (pp. 77--84); Gary Gruenhage, Perfectly normal compacta, cosmic spaces, and some partition problems (pp. 85--95); Klaas Pieter Hart and Jan van Mill, Open problems on $\beta\omega$ (pp. 97--125); Peter Nyikos, On first countable, countably compact spaces. III. The problem of obtaining separable noncompact examples (pp. 127--161); G. M. Reed, Set-theoretic problems in Moore spaces (pp. 163--181); Mary Ellen Rudin, Some conjectures (pp. 183--193); Jerry E. Vaughan, Small uncountable cardinals and topology (pp. 195--218); H. R. Bennett and J. Chaber, A survey of the class MOBI (pp. 221--229); H. R. Bennett and D. J. Lutzer, Problems in perfect ordered spaces (pp. 231--236); P. J. Collins, G. M. Reed and A. W. Roscoe, The point-countable base problem (pp. 237--250); Ben Fitzpatrick, Jr. and Hao Xuan Zhou, Some open problems in densely homogeneous spaces (pp. 251--259); Kenneth Kunen, Large homogeneous compact spaces (pp. 261--270); E. Michael [Ernest A. Michael], Some problems (pp. 271--278); Roman Pol, Questions in dimension theory (pp. 279--291); Howard Cook, W. T. Ingram and A. Lelek, Eleven annotated problems about continua (pp. 295--302); James T. Rogers, Jr., Tree-like curves and three classical problems (pp. 303--310); W. W. Comfort, Problems on topological groups and other homogeneous spaces (pp. 313--347); Jimmie D. Lawson and Michael Mislove, Problems in domain theory and topology (pp. 349--372); T. Y. Kong, R. Litherland and A. Rosenfeld [Azriel Rozenfeld], Problems in the topology of binary digital images (pp. 375--385); J.-J. Ch. Meyer and E. P. de Vink, On relating denotational and operational semantics for programming languages with recursion and concurrency (pp. 387--406); T. Dobrowolski and J. Mogilski, Problems on topological classification of incomplete metric spaces (pp. 409--429); Robert J. Daverman, Problems about finite-dimensional manifolds (pp. 431--455); Jerzy Dydak and Jack Segal, A list of open problems in shape theory (pp. 457--467); G. E. Carlsson, Problems on algebraic topology (pp. 469--486); Louis H. Kauffman, Problems in knot theory (pp. 487--522); James E. West, Open problems in infinite-dimensional topology (pp. 523--597); A. V. Arkhangelskii, Problems in $C\sb p$-theory (pp. 601--615); R. Daniel Mauldin, Problems in topology arising from analysis (pp. 617--629); Marcy Barge and Judy Kennedy, Continuum theory and topological dynamics (pp. 633--644); Sebastian van Strien, One-dimensional versus two-dimensional dynamics (pp. 645--654).

The book contains 1100 problems from areas of topology including set-theoretic topology, general topology, continua theory, topology and algebraic structures, topology and computer science, algebraic and geometric topology, topology arising from analysis, and dynamics. The problems are organized into subsections containing definitions of technical terms, background discussion, progress reports, as well as references to the relevant literature. The references appear up-to-date as many are listed as "to appear" or in preprint form.

The journal Topology and its Applications has agreed to provide a readily available source for determining the status of the various problems. Each issue of the journal will have space devoted to updating the status as progress is made on individual problems.

The comprehensiveness of the list of problems stretches far beyond the reviewer's areas of expertise. Reflecting on problems listed in the chapter titled Algebraic and geometric topology, which include many that have stymied the reviewer, and inferring that the remainder of the book is as up-to-date and thorough suggests that the authors have met or exceeded their stated goals.

This compendium is a marvelous addition to the literature, and the editors as well as the many individuals involved with developing the various sections are to be commended.

Reviewed by John J. Walsh