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Author : Werner Gahler,Horst Herrlich,Gerhard Preuss
Publisher : Unknown
Page : 319 pages
File Size : 44,6 Mb
Release : 1992
Category : Topology
ISBN : OCLC:29847631
Author : Werner Gähler,Horst Herrlich,Gerhard Preuss
Publisher : Wiley-VCH
Page : 328 pages
File Size : 50,8 Mb
Release : 1992-10-23
Category : Mathematics
ISBN : STANFORD:36105002336522
This volume contains the main part of the lectures contributed to the conference. They reflect the new trends of development in general topology.
Author : R.A. Alo,R.W. Heath,J. Nagata
Publisher : Springer
Page : 669 pages
File Size : 45,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540383239
Sponsored by Carnegie-Mellon University and the University of Pittsburgh
Author : M. Husek,J. van Mill
Publisher : Elsevier
Page : 652 pages
File Size : 54,5 Mb
Release : 2002-11-13
Category : Mathematics
ISBN : 9780444509802
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.
Author : K.P. Hart,J. van Mill,P. Simon
Publisher : Springer Science & Business Media
Page : 903 pages
File Size : 41,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9789462390249
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.
Author : Ulrich Höhle
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 45,7 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9781461516170
The 20th Century brought the rise of General Topology. It arose from the effort to establish a solid base for Analysis and it is intimately related to the success of set theory. Many Valued Topology and Its Applications seeks to extend the field by taking the monadic axioms of general topology seriously and continuing the theory of topological spaces as topological space objects within an almost completely ordered monad in a given base category C. The richness of this theory is shown by the fundamental fact that the category of topological space objects in a complete and cocomplete (epi, extremal mono)-category C is topological over C in the sense of J. Adamek, H. Herrlich, and G.E. Strecker. Moreover, a careful, categorical study of the most important topological notions and concepts is given - e.g., density, closedness of extremal subobjects, Hausdorff's separation axiom, regularity, and compactness. An interpretation of these structures, not only by the ordinary filter monad, but also by many valued filter monads, underlines the richness of the explained theory and gives rise to new concrete concepts of topological spaces - so-called many valued topological spaces. Hence, many valued topological spaces play a significant role in various fields of mathematics - e.g., in the theory of locales, convergence spaces, stochastic processes, and smooth Borel probability measures. In its first part, the book develops the necessary categorical basis for general topology. In the second part, the previously given categorical concepts are applied to monadic settings determined by many valued filter monads. The third part comprises various applications of many valued topologies to probability theory and statistics as well as to non-classical model theory. These applications illustrate the significance of many valued topology for further research work in these important fields.
Author : C.E. Aull,R. Lowen
Publisher : Springer Science & Business Media
Page : 381 pages
File Size : 46,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401704687
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.
Author : M. Husek,J. van Mill
Publisher : Elsevier
Page : 651 pages
File Size : 52,5 Mb
Release : 2002-11-13
Category : Mathematics
ISBN : 9780080929958
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. 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.
Author : Frdric Mynard,Elliott Pearl
Publisher : American Mathematical Soc.
Page : 395 pages
File Size : 41,7 Mb
Release : 2009-05-15
Category : Mathematics
ISBN : 9780821842799
The purpose of this collection is to guide the non-specialist through the basic theory of various generalizations of topology, starting with clear motivations for their introduction. Structures considered include closure spaces, convergence spaces, proximity spaces, quasi-uniform spaces, merotopic spaces, nearness and filter spaces, semi-uniform convergence spaces, and approach spaces. Each chapter is self-contained and accessible to the graduate student, and focuses on motivations to introduce the generalization of topologies considered, presenting examples where desirable properties are not present in the realm of topologies and the problem is remedied in the more general context. Then, enough material will be covered to prepare the reader for more advanced papers on the topic. While category theory is not the focus of the book, it is a convenient language to study these structures and, while kept as a tool rather than an object of study, will be used throughout the book. For this reason, the book contains an introductory chapter on categorical topology.
Author : Eraldo Giuli
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 46,5 Mb
Release : 1996-06-30
Category : Mathematics
ISBN : 0792340493
This volume contains selected papers presented at the International Workshop on Categorical Topology, held at the University of L'Aquila, L'Aquila, Italy from August 31 to September 4, 1994. The collection should be of interest to mathematicians whose work involves category theory.
Author : K.P. Hart,Jun-iti Nagata,J.E. Vaughan
Publisher : Elsevier
Page : 536 pages
File Size : 52,9 Mb
Release : 2003-11-18
Category : Mathematics
ISBN : 0080530869
This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: • More terms from General Topology than any other book ever published • Short and informative articles • Authors include the majority of top researchers in the field • Extensive indexing of terms
Author : A. Arhangel'skii
Publisher : Unknown
Page : 651 pages
File Size : 43,9 Mb
Release : 2002
Category : Electronic
ISBN : OCLC:1024265928
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 fol.
Author : R. M. Dudley
Publisher : Cambridge University Press
Page : 570 pages
File Size : 44,8 Mb
Release : 2002-10-14
Category : Mathematics
ISBN : 0521007542
This classic text offers a clear exposition of modern probability theory.
Author : Dirk Hofmann,Gavin J. Seal,Walter Tholen
Publisher : Cambridge University Press
Page : 523 pages
File Size : 43,7 Mb
Release : 2014-07-31
Category : Mathematics
ISBN : 9781107063945
Based on lax-algebraic and categorical methods, Monoidal Topology provides a unified theory for metric and topological structures with far-reaching applications.
Author : Szymon Dolecki,Frédéric Mynard
Publisher : World Scientific Publishing Company
Page : 568 pages
File Size : 49,9 Mb
Release : 2016-05-13
Category : Mathematics
ISBN : 9789814571548
This textbook is an alternative to a classical introductory book in point-set topology. The approach, however, is radically different from the classical one. It is based on convergence rather than on open and closed sets. Convergence of filters is a natural generalization of the basic and well-known concept of convergence of sequences, so that convergence theory is more natural and intuitive to many, perhaps most, students than classical topology. On the other hand, the framework of convergence is easier, more powerful and far-reaching which highlights a need for a theory of convergence in various branches of analysis. Convergence theory for filters is gradually introduced and systematically developed. Topological spaces are presented as a special subclass of convergence spaces of particular interest, but a large part of the material usually developed in a topology textbook is treated in the larger realm of convergence spaces.
