Handbook Of The History Of General Topology
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Handbook Of The History Of General Topology
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Author : C.E. Aull
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-03-31
Handbook Of The History Of General Topology written by C.E. Aull 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 1997-03-31 with Mathematics categories.
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.
Handbook Of The History Of General Topology
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Author : C.E. Aull
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Handbook Of The History Of General Topology written by C.E. Aull 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 2013-04-18 with Mathematics categories.
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.
History Of Topology
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Author : I.M. James
language : en
Publisher: Elsevier
Release Date : 1999-08-24
History Of Topology written by I.M. James and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-24 with Mathematics categories.
Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Beyond Topology
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Author : Frdric Mynard
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-05-15
Beyond Topology written by Frdric Mynard 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 2009-05-15 with Mathematics categories.
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.
Topology
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Author : K. Parthasarathy
language : en
Publisher: Springer Nature
Release Date : 2022-07-09
Topology written by K. Parthasarathy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-09 with Mathematics categories.
This book starts with a discussion of the classical intermediate value theorem and some of its uncommon “topological” consequences as an appetizer to whet the interest of the reader. It is a concise introduction to topology with a tinge of historical perspective, as the author’s perception is that learning mathematics should be spiced up with a dash of historical development. All the basics of general topology that a student of mathematics would need are discussed, and glimpses of the beginnings of algebraic and combinatorial methods in topology are provided. All the standard material on basic set topology is presented, with the treatment being sometimes new. This is followed by some of the classical, important topological results on Euclidean spaces (the higher-dimensional intermediate value theorem of Poincaré–Miranda, Brouwer’s fixed-point theorem, the no-retract theorem, theorems on invariance of domain and dimension, Borsuk’s antipodal theorem, the Borsuk–Ulam theorem and the Lusternik–Schnirelmann–Borsuk theorem), all proved by combinatorial methods. This material is not usually found in introductory books on topology. The book concludes with an introduction to homotopy, fundamental groups and covering spaces. Throughout, original formulations of concepts and major results are provided, along with English translations. Brief accounts of historical developments and biographical sketches of the dramatis personae are provided. Problem solving being an indispensable process of learning, plenty of exercises are provided to hone the reader's mathematical skills. The book would be suitable for a first course in topology and also as a source for self-study for someone desirous of learning the subject. Familiarity with elementary real analysis and some felicity with the language of set theory and abstract mathematical reasoning would be adequate prerequisites for an intelligent study of the book.
History Of Banach Spaces And Linear Operators
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Author : Albrecht Pietsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31
History Of Banach Spaces And Linear Operators written by Albrecht Pietsch 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 2007-12-31 with Mathematics categories.
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
The Oxford Handbook Of The History Of Mathematics
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Author : Eleanor Robson
language : en
Publisher: OUP Oxford
Release Date : 2008-12-18
The Oxford Handbook Of The History Of Mathematics written by Eleanor Robson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-18 with Mathematics categories.
This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood. The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.
Generalized Metric Spaces And Mappings
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Author : Shou Lin
language : en
Publisher: Springer
Release Date : 2016-10-20
Generalized Metric Spaces And Mappings written by Shou Lin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-20 with Mathematics categories.
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.
Encyclopedia Of General Topology
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Author : K.P. Hart
language : en
Publisher: Elsevier
Release Date : 2003-11-18
Encyclopedia Of General Topology written by K.P. Hart and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-18 with Mathematics categories.
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
R L Moore
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Author : John Parker
language : en
Publisher: MAA
Release Date : 2005
R L Moore written by John Parker and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Biography & Autobiography categories.
R. L. Moore: Mathematician and Teacher presents a full and frank biography of a mathematician recognized as one of the principal figures in the 20th Century progression of the American school of point set topology. He was equally well known as creator of the Moore Method (no textbooks, no lectures, no conferring) in which there is a current and growing revival of interest and modified application under inquiry-based learning projects in both the United States and the United Kingdom. Parker draws on oral history, with first-person recollections from many leading figures in the American mathematics community of the last half-century. The story embraces some of the most famous and influential mathematical names in America and Europe from the late 1900s in what is undoubtedly a lively account of this controversial figure, once described as Mr. Chips with Attitude. He was the first American to become a Visiting Lecturer for the American Mathematical Society, was a member of the National Academy of Sciences, published 68 papers and a book that is still referred to seventy years later and that has been the subject of literally hundreds of papers by other mathematicians around the globe. Three of Moore's students followed him as president of the American Mathematical Society, and three others became vice-presidents. Five served as president of the Mathematical Association of America, and three became members of the National Academy of Sciences.