Ordinal Invariants in Topology PDF Download
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Author: V. Kannan
Publisher: American Mathematical Soc.
ISBN: 0821822454
Category : Mathematics
Languages : en
Pages : 173
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Book Description
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.
Author: V. Kannan
Publisher: American Mathematical Soc.
ISBN: 0821822454
Category : Mathematics
Languages : en
Pages : 173
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Book Description
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.
Author: D. Dikranjan
Publisher: Springer Science & Business Media
ISBN: 9401584001
Category : Mathematics
Languages : en
Pages : 373
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Book Description
Our motivation for gathering the material for this book over aperiod of seven years has been to unify and simplify ideas wh ich appeared in a sizable number of re search articles during the past two decades. More specifically, it has been our aim to provide the categorical foundations for extensive work that was published on the epimorphism- and cowellpoweredness problem, predominantly for categories of topological spaces. In doing so we found the categorical not ion of closure operators interesting enough to be studied for its own sake, as it unifies and describes other significant mathematical notions and since it leads to a never-ending stream of ex amples and applications in all areas of mathematics. These are somewhat arbitrarily restricted to topology, algebra and (a small part of) discrete mathematics in this book, although other areas, such as functional analysis, would provide an equally rich and interesting supply of examples. We also had to restrict the themes in our theoretical exposition. In spite of the fact that closure operators generalize the uni versal closure operations of abelian category theory and of topos- and sheaf theory, we chose to mention these aspects only en passant, in favour of the presentation of new results more closely related to our original intentions. We also needed to refrain from studying topological concepts, such as compactness, in the setting of an arbitrary closure-equipped category, although this topic appears prominently in the published literature involving closure operators.
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: Elliott M. Pearl
Publisher: Elsevier
ISBN: 0080475299
Category : Mathematics
Languages : en
Pages : 777
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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: E. E. Grace
Publisher:
ISBN:
Category : Topological algebras
Languages : en
Pages : 360
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Book Description
Author: Josef Novák
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 548
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Book Description
Author: A.V. Arkhangel'skii
Publisher: Springer Science & Business Media
ISBN: 3642612652
Category : Mathematics
Languages : en
Pages : 210
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Book Description
This is the first of the encyclopaedia volumes devoted to general topology. It has two parts. The first outlines the basic concepts and constructions of general topology, including several topics which have not previously been covered in English language texts. The second part presents a survey of dimension theory, from the very beginnings to the most important recent developments. The principal ideas and methods are treated in detail, and the main results are provided with sketches of proofs. The authors have suceeded admirably in the difficult task of writing a book which will not only be accessible to the general scientist and the undergraduate, but will also appeal to the professional mathematician. The authors' efforts to detail the relationship between more specialized topics and the central themes of topology give the book a broad scholarly appeal which far transcends narrow disciplinary lines.
Author: American Mathematical Society
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 890
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Book Description
Contains the material formerly published in even-numbered issues of the Bulletin of the American Mathematical Society.
Author: Zbigniew Semadeni
Publisher:
ISBN:
Category : Banach spaces
Languages : en
Pages : 594
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Book Description
Author: Shou Lin
Publisher: Springer
ISBN: 9462392161
Category : Mathematics
Languages : en
Pages : 341
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Book Description
The idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.
