Surveys in General Topology

Author: George M. Reed

Publisher: Academic Press

ISBN: 148326386X

Category: Mathematics

Page: 572

View: 8396


Surveys in General Topology presents topics relating to general topology ranging from closed mappings and ultrafilters to covering and separation properties of box products. Ordered topological spaces and the use of combinatorial techniques in functional analysis are also considered, along with product spaces and weakly compact subsets of Banach spaces. Applications of stationary sets in topology are presented as well. Comprised of 15 chapters, this volume begins with an analysis of some of the techniques and results in the area of closed mappings, followed by a discussion on the theory of ultrafilters. The reader is then introduced to the question of when a box product of compact spaces is paracompact, and how badly a box product of compact or metrizable spaces can fail to be normal. Subsequent chapters focus on the transfinite dimension; the properties of metacompactness, submetacompactness, and subparacompactness; the dimension of ordered topological spaces; the use of combinatorial techniques for the treatment and solution of fundamental problems in functional analysis, particularly in the isomorphic theory of Banach spaces; and order-theoretic base axioms. This monograph will be of significant value both to researchers in general topology and to mathematicians outside the field who wish an overview of current topics and techniques.

Recent Progress in General Topology II

Author: Miroslav Hušek,J. van Mill

Publisher: Elsevier

ISBN: 0444509801

Category: Mathematics

Page: 638

View: 3865


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. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs slightly from those chosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (including Infinite-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. Mardeŝić, 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.

Handbook of the History of General Topology

Author: C.E. Aull,R. Lowen

Publisher: Springer Science & Business Media

ISBN: 9401717567

Category: Mathematics

Page: 410

View: 1999


This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.

Recent Progress in General Topology III

Author: K.P. Hart,J. van Mill,P. Simon

Publisher: Springer Science & Business Media

ISBN: 946239024X

Category: Mathematics

Page: 903

View: 1969


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, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

Topology I

General Survey

Author: S.P. Novikov

Publisher: Springer Science & Business Media

ISBN: 3662105799

Category: Mathematics

Page: 322

View: 5545


This up-to-date survey of the whole field of topology is the flagship of the topology subseries of the Encyclopaedia. The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present frontiers of research.

Pseudocompact Topological Spaces

A Survey of Classic and New Results with Open Problems

Author: Michael Hrušák,Ángel Tamariz-Mascarúa,Mikhail Tkachenko

Publisher: Springer

ISBN: 3319916807

Category: Mathematics

Page: 299

View: 3642


This book, intended for postgraduate students and researchers, presents many results of historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of pseudocompactness which generalizes a property of compact subsets of the real line. A topological space is pseudocompact if the range of any real-valued, continuous function defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures. The collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. In addition, the text examines new lines of research that have been at the forefront of mathematics. There is, as yet, no text that systematically compiles and develops the extensive theory of pseudocompact spaces, making this book an essential asset for anyone in the field of topology.

Open Problems in Topology II

Author: Elliott M. Pearl

Publisher: Elsevier

ISBN: 9780080475295

Category: Mathematics

Page: 776

View: 7251


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. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world

Surveys in Contemporary Mathematics

Author: Nicholas Young,Yemon Choi

Publisher: Cambridge University Press

ISBN: 0521705649

Category: Mathematics

Page: 361

View: 4511


A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.

General Topology

Author: Stephen Willard

Publisher: Courier Corporation

ISBN: 9780486434797

Category: Mathematics

Page: 369

View: 4415


Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.

Surveys in Combinatorics, 1999

Author: J. D. Lamb,D. A. Preece,Donald Arthur Preece,N. J. Hitchin

Publisher: Cambridge University Press

ISBN: 9780521653763

Category: Mathematics

Page: 298

View: 1317


This volume, first published in 1999, is a valuable resource on combinatorics for graduate students and researchers.

Algebraic Topology

Homology and Cohomology

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486462390

Category: Mathematics

Page: 272

View: 1284


Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.

Maß und Kategorie

Author: J.C. Oxtoby

Publisher: Springer-Verlag

ISBN: 364296074X

Category: Mathematics

Page: 112

View: 1862


Dieses Buch behandelt hauptsächlich zwei Themenkreise: Der Bairesche Kategorie-Satz als Hilfsmittel für Existenzbeweise sowie Die "Dualität" zwischen Maß und Kategorie. Die Kategorie-Methode wird durch viele typische Anwendungen erläutert; die Analogie, die zwischen Maß und Kategorie besteht, wird nach den verschiedensten Richtungen hin genauer untersucht. Hierzu findet der Leser eine kurze Einführung in die Grundlagen der metrischen Topologie; außerdem werden grundlegende Eigenschaften des Lebesgue schen Maßes hergeleitet. Es zeigt sich, daß die Lebesguesche Integrationstheorie für unsere Zwecke nicht erforderlich ist, sondern daß das Riemannsche Integral ausreicht. Weiter werden einige Begriffe aus der allgemeinen Maßtheorie und Topologie eingeführt; dies geschieht jedoch nicht nur der größeren Allgemeinheit wegen. Es erübrigt sich fast zu erwähnen, daß sich die Bezeichnung "Kategorie" stets auf "Bairesche Kategorie" be zieht; sie hat nichts zu tun mit dem in der homologischen Algebra verwendeten Begriff der Kategorie. Beim Leser werden lediglich grundlegende Kenntnisse aus der Analysis und eine gewisse Vertrautheit mit der Mengenlehre vorausgesetzt. Für die hier untersuchten Probleme bietet sich in natürlicher Weise die mengentheoretische Formulierung an. Das vorlie gende Buch ist als Einführung in dieses Gebiet der Analysis gedacht. Man könnte es als Ergänzung zur üblichen Grundvorlesung über reelle Analysis, als Grundlage für ein Se minar oder auch zum selbständigen Studium verwenden. Bei diesem Buch handelt es sich vorwiegend um eine zusammenfassende Darstellung; jedoch finden sich in ihm auch einige Verfeinerungen bekannter Resultate, namentlich Satz 15.6 und Aussage 20.4. Das Literaturverzeichnis erhebt keinen Anspruch auf Vollständigkeit. Häufig werden Werke zitiert, die weitere Literaturangaben enthalten.

The Renaissance of General Relativity and Cosmology

A Survey to Celebrate the 65th Birthday of Dennis Sciama

Author: George Ellis,Antonio Lanza,John Miller

Publisher: Cambridge University Press

ISBN: 9780521021081

Category: Science

Page: 344

View: 7338


The past forty years have been a time of spectacular development in the study of general relativity and cosmology. A special role in this has been played by the influential research groups led by Dennis Sciama in Cambridge, Oxford, and Trieste. In April 1992 many of his ex-students and collaborators came to Trieste (where he is currently Professor) for a review meeting to celebrate his 65th birthday. This book consists of written versions of the talks presented which, taken together, comprise an authoritative overview of developments which have taken place during his career to date. The topics covered include fundamental questions in general relativity and cosmology, black holes, active galactic nuclei, galactic structure, dark matter, and large scale structure.