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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: Michael Hrušák
Publisher: Springer
ISBN: 3319916807
Category : Mathematics
Languages : en
Pages : 299
Get Book
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: David Alan Lamb
Publisher:
ISBN:
Category :
Languages : en
Pages : 98
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Book Description
Author: Dikran N. Dikranjan
Publisher: American Mathematical Soc.
ISBN: 0821806297
Category : Compact groups
Languages : en
Pages : 101
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Book Description
The fundamental property of compact spaces - that continuous functions defined on compact spaces are bounded - served as a motivation for E. Hewitt to introduce the notion of a pseudocompact space. The class of pseudocompact spaces proved to be of fundamental importance in set-theoretic topology and its applications. This clear and self-contained exposition offers a comprehensive treatment of the question, When does a group admit an introduction of a pseudocompact Hausdorff topology that makes group operations continuous? Equivalently, what is the algebraic structure of a pseudocompact Hausdorff group? The authors have adopted a unifying approach that covers all known results and leads to new ones, Results in the book are free of any additional set-theoretic assumptions.
Author: Sergeĭ Petrovich Novikov
Publisher: American Mathematical Soc.
ISBN: 9780821831519
Category : Mathematics
Languages : en
Pages : 266
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Book Description
The Proceedings of an international topology conference - this book covrs various aspects of general algebraic, and low-dimensional topology.
Author: Lynn Arthur Steen
Publisher: Courier Corporation
ISBN: 0486319296
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Author: Douglas Bridges
Publisher: Cambridge University Press
ISBN: 100904141X
Category : Mathematics
Languages : en
Pages : 864
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Book Description
Constructive mathematics – mathematics in which 'there exists' always means 'we can construct' – is enjoying a renaissance. fifty years on from Bishop's groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of mathematics and to have profound influence in theoretical computer science. This handbook gives the most complete overview of modern constructive mathematics, with contributions from leading specialists surveying the subject's myriad aspects. Major themes include: constructive algebra and geometry, constructive analysis, constructive topology, constructive logic and foundations of mathematics, and computational aspects of constructive mathematics. A series of introductory chapters provides graduate students and other newcomers to the subject with foundations for the surveys that follow. Edited by four of the most eminent experts in the field, this is an indispensable reference for constructive mathematicians and a fascinating vista of modern constructivism for the increasing number of researchers interested in constructive approaches.
Author: K.P. Hart
Publisher: Elsevier
ISBN: 0080530869
Category : Mathematics
Languages : en
Pages : 537
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Book Description
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: 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: A. V. Arhangel' skii
Publisher: Springer Science & Business Media
ISBN: 3642770304
Category : Mathematics
Languages : en
Pages : 265
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Book Description
Compactness is related to a number of fundamental concepts of mathemat ics. Particularly important are compact Hausdorff spaces or compacta. Com pactness appeared in mathematics for the first time as one of the main topo logical properties of an interval, a square, a sphere and any closed, bounded subset of a finite dimensional Euclidean space. Once it was realized that pre cisely this property was responsible for a series of fundamental facts related to those sets such as boundedness and uniform continuity of continuous func tions defined on them, compactness was given an abstract definition in the language of general topology reaching far beyond the class of metric spaces. This immensely extended the realm of application of this concept (including in particular, function spaces of quite general nature). The fact, that general topology provided an adequate language for a description of the concept of compactness and secured a natural medium for its harmonious development is a major credit to this area of mathematics. The final formulation of a general definition of compactness and the creation of the foundations of the theory of compact topological spaces are due to P.S. Aleksandrov and Urysohn (see Aleksandrov and Urysohn (1971)).
Author: Robert A. McCoy
Publisher: Springer
ISBN: 3319770543
Category : Mathematics
Languages : en
Pages : 106
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Book Description
This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing literature. The goal of this monograph is to provide an extensive study of the uniform, fine and graph topologies on the space C(X,Y) of all continuous functions from a Tychonoff space X to a metric space (Y,d); and the uniform and fine topologies on the space H(X) of all self-homeomorphisms on a metric space (X,d). The subject matter of this monograph is significant from the theoretical viewpoint, but also has applications in areas such as analysis, approximation theory and differential topology. Written in an accessible style, this book will be of interest to researchers as well as graduate students in this vibrant research area.
