Topology Now
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Topology Now
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Author : Robert Messer
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-10
Topology Now written by Robert Messer 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 2018-10-10 with categories.
Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.
Topology Now
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Author : Robert Messer
language : en
Publisher: Mathematical Association of America
Release Date : 2006-05-11
Topology Now written by Robert Messer and has been published by Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-11 with Mathematics categories.
Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.
Elementary Topology
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Author : Michael C. Gemignani
language : en
Publisher: Courier Corporation
Release Date : 1990-01-01
Elementary Topology written by Michael C. Gemignani and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
Topology is one of the most rapidly expanding areas of mathematical thought: while its roots are in geometry and analysis, topology now serves as a powerful tool in almost every sphere of mathematical study. This book is intended as a first text in topology, accessible to readers with at least three semesters of a calculus and analytic geometry sequence. In addition to superb coverage of the fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, and other essentials, Elementary Topology gives added perspective as the author demonstrates how abstract topological notions developed from classical mathematics. For this second edition, numerous exercises have been added as well as a section dealing with paracompactness and complete regularity. The Appendix on infinite products has been extended to include the general Tychonoff theorem; a proof of the Tychonoff theorem which does not depend on the theory of convergence has also been added in Chapter 7.
Modern General Topology
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Author : J.-I. Nagata
language : en
Publisher: Elsevier
Release Date : 1985-11-01
Modern General Topology written by J.-I. Nagata and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-11-01 with Mathematics categories.
This classic work has been fundamentally revised to take account of recent developments in general topology. The first three chapters remain unchanged except for numerous minor corrections and additional exercises, but chapters IV-VII and the new chapter VIII cover the rapid changes that have occurred since 1968 when the first edition appeared. The reader will find many new topics in chapters IV-VIII, e.g. theory of Wallmann-Shanin's compactification, realcompact space, various generalizations of paracompactness, generalized metric spaces, Dugundji type extension theory, linearly ordered topological space, theory of cardinal functions, dyadic space, etc., that were, in the author's opinion, mostly special or isolated topics some twenty years ago but now settle down into the mainstream of general topology.
Knots And Primes
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Author : Masanori Morishita
language : en
Publisher: Springer
Release Date : 2024-02-28
Knots And Primes written by Masanori Morishita and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-28 with Mathematics categories.
This book provides a foundation for arithmetic topology, a new branch of mathematics that investigates the analogies between the topology of knots, 3-manifolds, and the arithmetic of number fields. Arithmetic topology is now becoming a powerful guiding principle and driving force to obtain parallel results and new insights between 3-dimensional geometry and number theory. After an informative introduction to Gauss' work, in which arithmetic topology originated, the text reviews a background from both topology and number theory. The analogy between knots in 3-manifolds and primes in number rings, the founding principle of the subject, is based on the étale topological interpretation of primes and number rings. On the basis of this principle, the text explores systematically intimate analogies and parallel results of various concepts and theories between 3-dimensional topology and number theory. The presentation of these analogies begins at an elementary level, gradually building to advanced theories in later chapters. Many results presented here are new and original. References are clearly provided if necessary, and many examples and illustrations are included. Some useful problems are also given for future research. All these components make the book useful for graduate students and researchers in number theory, low dimensional topology, and geometry. This second edition is a corrected and enlarged version of the original one. Misprints and mistakes in the first edition are corrected, references are updated, and some expositions are improved. Because of the remarkable developments in arithmetic topology after the publication of the first edition, the present edition includes two new chapters. One is concerned with idelic class field theory for 3-manifolds and number fields. The other deals with topological and arithmetic Dijkgraaf–Witten theory, which supports a new bridge between arithmetic topology and mathematical physics.
Modern General Topology
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Author : Jun-iti Nagata
language : en
Publisher: North-Holland
Release Date : 1974
Modern General Topology written by Jun-iti Nagata and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
This classic work has been fundamentally revised to take account of recent developments in general topology. The first three chapters remain unchanged except for numerous minor corrections and additional exercises, but chapters IV-VII and the new chapter VIII cover the rapid changes that have occurred since 1968 when the first edition appeared. The reader will find many new topics in chapters IV-VIII, e.g. theory of Wallmann-Shanin's compactification, realcompact space, various generalizations of paracompactness, generalized metric spaces, Dugundji type extension theory, linearly ordered topological space, theory of cardinal functions, dyadic space, etc., that were, in the author's opinion, mostly special or isolated topics some twenty years ago but now settle down into the mainstream of general topology.
General Topology
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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-08-03
General Topology written by N. Bourbaki 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 1998-08-03 with Mathematics categories.
This is the softcover reprint of the English translation of 1971 (available from Springer since 1989) of the first 4 chapters of Bourbaki's Topologie générale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structures are introduced and applied to topological groups. Real numbers are constructed and their properties established. Part II, comprising the later chapters, Ch. 5-10, is also available in English in softcover.
Dynamic Topology
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Author : G. Whyburn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Dynamic Topology written by G. Whyburn 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 2012-12-06 with Mathematics categories.
It is a privilege for me to write a foreword for this unusual book. The book is not primarily a reference work although many of the ideas and proofs are explained more clearly here than in any other source that I know. Nor is this a text of the customary sort. It is rather a record of a particular course and Gordon Whyburn's special method of teaching it. Perhaps the easiest way to describe the course and the method is to relate my own personal experience with a forerunner of this same course in the academic year 1937-1938. At that time, the course was offered every other year with a following course in algebraic topology on alternate years. There were five of us enrolled, and on the average we knew less mathematics than is now routinely given in a junior course in analysis. Whyburn's purpose, as we learned, was to prepare us in minimal time for research in the areas in which he was inter ested. His method was remarkable.
Topology
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Author : Stefan Waldmann
language : en
Publisher: Springer
Release Date : 2014-08-05
Topology written by Stefan Waldmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-05 with Mathematics categories.
This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs. While there are already many excellent monographs on general topology, most of them are too large for a first bachelor course. Topology fills this gap and can be either used for self-study or as the basis of a topology course.
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.