Recent Progress in General Topology II

Editors: M. Hušek and J. van Mill
Publisher:
Elsevier (North-Holland)
Year: 2002
Review:
AMS review

Description

The book presents surveys describing recent developments in most of the primary subfields of General Topology and its applications to Algebra and Analysis during the last decade. It follows freely the previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared in connection with the Prague Topological Symposium, held in 2001. Over the past 10 years, the focus in General Topology has changed and therefore the selection of topics differs slightly from those chosen in 1992. The following areas have experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (including Infinite-Dimensional Topology and the Geometry of Banach Spaces) and are covered in this book.

Apart from surveys, the book contains several historical essays written by such eminent topologists as: R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardesic, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book is included.

Contents

Introduction.
Topological invariants in algebraic environment (A.V. Arhangel'skii).
Matrices and ultrafilters (J. Baker, K. Kunen).
Recent developments in the topology of ordered spaces (H.R. Bennett, D.J. Lutzer).
Infinite-dimensional topology (J.J. Dijkstra, J. van Mill).
Recent results in set-theoretical topology (A. Dow).
Topics in topological dynamics, 1991 to 2001 (E. Glasner).
Banach spaces of continuous functions on compact spaces (G. Godefroy).
Metrizable spaces and generalizations (G. Gruenhage).
Recent progress in the topological theory of semigroups and the algebra of S (N. Hindman, D. Strauss).
Recent progress in hyperspace topologies (L'. Hola, J. Pelant).
Some topics in geometric topology (K. Kawamura).
Quasi-uniform spaces in the year 2001 (H.-P. Kunzi).
Function spaces (W. Marciszewski).
Topology and domain theory (K. Martin, M.W. Mislove, G.M. Reed).
Topics in dimension theory (R. Pol, H. Torunczyk).
Continuous selections of multivalued mappings (D. Repovs, P.V. Semenov).
Convergence in the presence of algebraic structure (D. Shakhmatov).
Descriptive set theory in topology (S. Solecki).
Topological groups: between compactness and o-boundedness (M. Tkachenko).
Essays (R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardesic, J. Nagata, M.E. Rudin, Yu.M. Smirnov, reminiscences of L. Vietoris).
List of open problems and questions.
Author index
Special symbols
Subject index