Ordinal Invariants in Topology PDF Download

Author: V. Kannan
Publisher: American Mathematical Soc.
ISBN: 0821822454
Category : Mathematics
Languages : en
Pages : 164

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Book Description

Author: K. Kunen
Publisher: Elsevier
ISBN: 148329515X
Category : Mathematics
Languages : en
Pages : 1282

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Book Description
This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest. In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

Author: M. Husek
Publisher: Elsevier
ISBN: 0080934439
Category : Mathematics
Languages : en
Pages : 808

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Book Description
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.

Author: Juris Steprans
Publisher: Springer
ISBN: 3540467955
Category : Mathematics
Languages : en
Pages : 233

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Book Description
The Set Theory and Applications meeting at York University, Ontario, featured both contributed talks and a series of invited lectures on topics central to set theory and to general topology. These proceedings contain a selection of the resulting papers, mostly announcing new unpublished results.

Author: Michael Hrušák
Publisher: Springer
ISBN: 3319916807
Category : Mathematics
Languages : en
Pages : 299

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Book Description
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.

Author: K.P. Hart
Publisher: Springer Science & Business Media
ISBN: 946239024X
Category : Mathematics
Languages : en
Pages : 903

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Book 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, 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: Szymon Dolecki
Publisher: World Scientific
ISBN: 9811232121
Category : Mathematics
Languages : en
Pages : 733

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Book Description
Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more.The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge.Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book — from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory.The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers.Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.

Author: Elliott M. Pearl
Publisher: Elsevier
ISBN: 9780080475295
Category : Mathematics
Languages : en
Pages : 776

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Book Description
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

Author: Josef Novák
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 548

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Book Description

Author: W Gähler
Publisher: World Scientific
ISBN: 981448170X
Category : Mathematics
Languages : en
Pages : 356

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Book Description
The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich — one of the leading category theorists of the world — to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst Herrlich's publications. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:On Boole's Booleanness (B Banaschewski)Homeomorphically Closed Nearness Spaces (H L Bentley & J W Carlson)The Tensor Product of Orthomodular Posets (R Börger)Saturated Collections of Metrics (E Colebunders et al.)Topological Structures in Logics (W Gähler)The Structure of Affine Algebraic Sets (E Giuli)A Characterization of Co-Retracts of Functional Structures (R Kaschek)Introducing Lagois Correspondences (A Melton)On Coalgebras which are Algebras (H-E Porst & C Dzierzon)Fibrewise Sobriety (G Richter & A Vauth)and other papers Readership: Graduate students, researchers, academics and lecturers in mathematics and computer science. Keywords:Category Theory;Algebra;Logic;Topology;Fuzzy Structures;Computer Science