Recent progress in general topology
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Recent progress in general topology
North-Holland, 1992-
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注記
Papers from Prague Toposym 1991, held in Prague, Czechoslovakia, Aug. 19-23, 1991
Includes bibliographical references and index
内容説明・目次
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2 ISBN 9780444509802
内容説明
The book presents surveys describing recent developments in most of the primary subfields ofGeneral Topology and its applications to Algebra and Analysis during the last decade. It follows freelythe 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 inconnection with the Prague Topological Symposium, held in 2001. During the last 10 years the focusin General Topology changed and therefore the selection of topics differs slightly from thosechosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (includingInfinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as:R.D. Anderson, W.W. Comfort, M. Henriksen, S. Marde i , 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 are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.
目次
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. Repov , 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. Marde i , J. Nagata, M.E. Rudin, Yu.M. Smirnov, reminiscences of L. Vietoris).List of open problems and questions.Author indexSpecial symbolsSubject index
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ISBN 9780444896742
内容説明
These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan, North-Holland, 1984), which gives an almost complete picture of the state of the art of Set Theoretic Topology before 1984. In the present volume several important developments are surveyed that surfaced in the period 1984-1991.This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990). Solutions to some of the original 1100 open problems are discussed and new problems are posed.
目次
Introduction. Contents. Cp-theory (A.V. Arkhangel'ski ). Topological Groups and Semigroups (W.W. Comfort, K.-H. Hofmann, D. Remus). Topological Classification of Infinite-Dimensional Spaces with Absorbers (J.J. Dijkstra, J. van Mill). Set Theory in Topology (A. Dow). Sequential Convergence Spaces (R. Fri , V. Koutnik). Topology and Differentiation Theory (A. Froelicher, A. Kriegl). Generalized Metric Spaces and Metrization (G. Gruenhage). Descriptive Topology (R.W. Hansell). The ech-Stone Compactification of the Real Line (K.P. Hart). Special Metrics (Y. Hattori, J. Nagata). Categorical Topology (H. Herrlich, M. Husek). Extensions of Mappings (T. Hoshina). Cardinal Functions (I. Juhasz). Covering Properties (H.J.K. Junnila). Continuum Theory (J.C. Mayer, L.G. Oversteegen). Banach Spaces and Topology II (S. Mercourakis, S. Negrepontis). Convergence in Topology (P.J. Nyikos). Compact Spaces and Their Generalizations (D.B. Shakhmatov). Abstract Topological Dynamics (J. de Vries). The Construction of Topological Spaces (S. Watson). Index.
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