Ordinal Invariants For Topological Spaces

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Ordinal Invariants In Topology

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Author : V. Kannan
language : en
Publisher: American Mathematical Soc.
Release Date : 1981

Ordinal Invariants In Topology written by V. Kannan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.

In this work we show that almost all useful ordinal invariants in topology studied until now (such as derived length of scattered spaces, sequential order of sequential spaces, etc.) can be brought under the single heading of what we call the order of a map. This helps us to perceive some close connections among apparently unrelated corners of general topology, to view the known concepts from different angles and to obtain a lot of information about the particular cases.

Ordinal Invariants For Topological Spaces

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Author : A. B. Arhangelśkiĭ
language : en
Publisher:
Release Date : 1967

Ordinal Invariants For Topological Spaces written by A. B. Arhangelśkiĭ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Invariants categories.

Topological Invariants Of Stratified Spaces

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Author : Markus Banagl
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-16

Topological Invariants Of Stratified Spaces written by Markus Banagl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-16 with Mathematics categories.

The central theme of this book is the restoration of Poincaré duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety. Highlights include complete and detailed proofs of decomposition theorems for self-dual sheaves, explanation of methods for computing twisted characteristic classes and an introduction to the author's theory of non-Witt spaces and Lagrangian structures.

Pseudocompact Topological Spaces

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Author : Michael Hrušák
language : en
Publisher: Springer
Release Date : 2018-07-19

Pseudocompact Topological Spaces written by Michael Hrušák and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-19 with Mathematics categories.

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.

Handbook Of Set Theoretic Topology

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Author : K. Kunen
language : en
Publisher: Elsevier
Release Date : 2014-06-28

Handbook Of Set Theoretic Topology written by K. Kunen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.

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.

Recent Progress In General Topology

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Author : M. Husek
language : en
Publisher: Elsevier
Release Date : 1992-11-20

Recent Progress In General Topology written by M. Husek and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-20 with Mathematics categories.

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.

Set Theory And Its Applications

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Author : Juris Steprans
language : en
Publisher: Springer
Release Date : 2006-11-14

Set Theory And Its Applications written by Juris Steprans and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

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.

Invariants For Real Generated Uniform Topological And Algebraic Categories

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Author : K. A. Broughan
language : en
Publisher: Springer
Release Date : 2006-11-14

Invariants For Real Generated Uniform Topological And Algebraic Categories written by K. A. Broughan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Algebraic Local Invariants Of Topological Spaces

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Author : Sze-Tsen Hu
language : en
Publisher:
Release Date : 1958

Algebraic Local Invariants Of Topological Spaces written by Sze-Tsen Hu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Algebraic topology categories.

Royal Road To Topology A Convergence Of Filters

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Author : Szymon Dolecki
language : en
Publisher: World Scientific
Release Date : 2024-01-03

Royal Road To Topology A Convergence Of Filters written by Szymon Dolecki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-03 with Mathematics categories.

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.