Aspects Of Contemporary Topology

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Essential Topology

Author : Martin D. Crossley
Publisher : Springer Science & Business Media
ISBN 13 : 9781852337827
Total Pages : 244 pages
Book Rating : 4.3/5 (378 download)

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Book Synopsis Essential Topology by : Martin D. Crossley

Download or read book Essential Topology written by Martin D. Crossley and published by Springer Science & Business Media. This book was released on 2011-02-11 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.

Elements of Modern Topology

Author : Ronald Brown
Publisher :
ISBN 13 :
Total Pages : 382 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Elements of Modern Topology by : Ronald Brown

Download or read book Elements of Modern Topology written by Ronald Brown and published by . This book was released on 1968 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elements of Point Set Topology

Author : John D. Baum
Publisher : Courier Corporation
ISBN 13 : 0486668266
Total Pages : 164 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Elements of Point Set Topology by : John D. Baum

Download or read book Elements of Point Set Topology written by John D. Baum and published by Courier Corporation. This book was released on 1991-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

Modern Analysis and Topology

Author : Norman R. Howes
Publisher : Springer Science & Business Media
ISBN 13 : 1461208335
Total Pages : 434 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Modern Analysis and Topology by : Norman R. Howes

Download or read book Modern Analysis and Topology written by Norman R. Howes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. It is intended that the material be accessible to a reader of modest background. An advanced calculus course and an introductory topology course should be adequate. But it is also intended that this book be able to take the reader from that state to the frontiers of modern analysis and topology in-so-far as they can be done within the framework of uniform spaces. Modern analysis is usually developed in the setting of metric spaces although a great deal of harmonic analysis is done on topological groups and much offimctional analysis is done on various topological algebraic structures. All of these spaces are special cases of uniform spaces. Modern topology often involves spaces that are more general than uniform spaces, but the uniform spaces provide a setting general enough to investigate many of the most important ideas in modern topology, including the theories of Stone-Cech compactification, Hewitt Real-compactification and Tamano-Morita Para compactification, together with the theory of rings of continuous functions, while at the same time retaining a structure rich enough to support modern analysis.

Topology

Author : Tai-Danae Bradley
Publisher : MIT Press
ISBN 13 : 0262359626
Total Pages : 167 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Topology by : Tai-Danae Bradley

Download or read book Topology written by Tai-Danae Bradley and published by MIT Press. This book was released on 2020-08-18 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.

Modern General Topology

Author : Jun-Iti Nagata
Publisher : Elsevier
ISBN 13 : 1483278166
Total Pages : 376 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Modern General Topology by : Jun-Iti Nagata

Download or read book Modern General Topology written by Jun-Iti Nagata and published by Elsevier. This book was released on 2014-05-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume VII: Modern General Topology focuses on the processes, operations, principles, and approaches employed in pure and applied mathematics, including spaces, cardinal and ordinal numbers, and mappings. The publication first elaborates on set, cardinal and ordinal numbers, basic concepts in topological spaces, and various topological spaces. Discussions focus on metric space, axioms of countability, compact space and paracompact space, normal space and fully normal space, subspace, product space, quotient space, and inverse limit space, convergence, mapping, and open basis and neighborhood basis. The book then ponders on compact spaces and related topics, as well as product of compact spaces, compactification, extensions of the concept of compactness, and compact space and the lattice of continuous functions. The manuscript tackles paracompact spaces and related topics, metrizable spaces and related topics, and topics related to mappings. Topics include metric space, paracompact space, and continuous mapping, theory of inverse limit space, theory of selection, mapping space, imbedding, metrizability, uniform space, countably paracompact space, and modifications of the concept of paracompactness. The book is a valuable source of data for mathematicians and researchers interested in modern general topology.

Elements of Homology Theory

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
ISBN 13 : 0821838121
Total Pages : 432 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Elements of Homology Theory by : Viktor Vasilʹevich Prasolov

Download or read book Elements of Homology Theory written by Viktor Vasilʹevich Prasolov and published by American Mathematical Soc.. This book was released on 2007 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.

Topology and Groupoids

Author : Ronald Brown
Publisher : Booksurge Llc
ISBN 13 : 9781419627224
Total Pages : 512 pages
Book Rating : 4.6/5 (272 download)

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Book Synopsis Topology and Groupoids by : Ronald Brown

Download or read book Topology and Groupoids written by Ronald Brown and published by Booksurge Llc. This book was released on 2006 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation. The book is intended as a text for a two-semester course in topology and algebraic topology at the advanced undergraduate orbeginning graduate level. There are over 500 exercises, 114 figures, numerous diagrams. The general direction of the book is towardhomotopy theory with a geometric point of view. This book would providea more than adequate background for a standard algebraic topology coursethat begins with homology theory. For more information seewww.bangor.ac.uk/r.brown/topgpds.htmlThis version dated April 19, 2006, has a number of corrections made.

Essentials of Topology with Applications

Author : Steven G. Krantz
Publisher : CRC Press
ISBN 13 : 1420089757
Total Pages : 422 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Essentials of Topology with Applications by : Steven G. Krantz

Download or read book Essentials of Topology with Applications written by Steven G. Krantz and published by CRC Press. This book was released on 2009-07-28 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brings Readers Up to Speed in This Important and Rapidly Growing AreaSupported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological

Topologies of Power

Author : John Allen
Publisher : Routledge
ISBN 13 : 1136237666
Total Pages : 189 pages
Book Rating : 4.1/5 (362 download)

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Book Synopsis Topologies of Power by : John Allen

Download or read book Topologies of Power written by John Allen and published by Routledge. This book was released on 2016-01-13 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topologies of Power amounts to a radical departure in the way that power and space have been understood. It calls into question the very idea that power is simply extended across a given territory or network, and argues that power today has a new found ‘reach’. Topological shifts have subtly altered the reach of power, enabling governments, corporations and NGOs alike to register their presence through quieter, less brash forms of power than domination or overt control. In a world in which proximity and distance increasingly play across one another, topology offers an insight into how power remains continuous under transformation: the same but different in its ability to shape peoples’ lives. Drawing upon a range of political, economic and cultural illustrations, the book sets out a clear and accessible account of the topological workings of power in the contemporary moment. It will be invaluable for both students and academics in human geography, politics, sociology, and cultural studies.

Riemann, Topology, and Physics

Author : Michael I. Monastyrsky
Publisher : Springer Science & Business Media
ISBN 13 : 0817647791
Total Pages : 220 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Riemann, Topology, and Physics by : Michael I. Monastyrsky

Download or read book Riemann, Topology, and Physics written by Michael I. Monastyrsky and published by Springer Science & Business Media. This book was released on 2009-06-08 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The significantly expanded second edition of this book combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter.

A Concise Course in Algebraic Topology

Author : J. P. May
Publisher : University of Chicago Press
ISBN 13 : 9780226511832
Total Pages : 262 pages
Book Rating : 4.5/5 (118 download)

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Book Synopsis A Concise Course in Algebraic Topology by : J. P. May

Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Post-Soviet Social

Author : Stephen J. Collier
Publisher : Princeton University Press
ISBN 13 : 1400840422
Total Pages : 321 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Post-Soviet Social by : Stephen J. Collier

Download or read book Post-Soviet Social written by Stephen J. Collier and published by Princeton University Press. This book was released on 2011-08-08 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Soviet Union created a unique form of urban modernity, developing institutions of social provisioning for hundreds of millions of people in small and medium-sized industrial cities spread across a vast territory. After the collapse of socialism these institutions were profoundly shaken--casualties, in the eyes of many observers, of market-oriented reforms associated with neoliberalism and the Washington Consensus. In Post-Soviet Social, Stephen Collier examines reform in Russia beyond the Washington Consensus. He turns attention from the noisy battles over stabilization and privatization during the 1990s to subsequent reforms that grapple with the mundane details of pipes, wires, bureaucratic routines, and budgetary formulas that made up the Soviet social state. Drawing on Michel Foucault's lectures from the late 1970s, Post-Soviet Social uses the Russian case to examine neoliberalism as a central form of political rationality in contemporary societies. The book's basic finding--that neoliberal reforms provide a justification for redistribution and social welfare, and may work to preserve the norms and forms of social modernity--lays the groundwork for a critical revision of conventional understandings of these topics.

Schaum's Outline of Theory and Problems of General Topology

Author : Seymour Lipschutz
Publisher :
ISBN 13 :
Total Pages : 239 pages
Book Rating : 4.:/5 (85 download)

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Book Synopsis Schaum's Outline of Theory and Problems of General Topology by : Seymour Lipschutz

Download or read book Schaum's Outline of Theory and Problems of General Topology written by Seymour Lipschutz and published by . This book was released on 1987 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Topology: An Intuitive Approach

Author : Hajime Satō
Publisher : American Mathematical Soc.
ISBN 13 : 9780821810460
Total Pages : 144 pages
Book Rating : 4.8/5 (14 download)

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Book Synopsis Algebraic Topology: An Intuitive Approach by : Hajime Satō

Download or read book Algebraic Topology: An Intuitive Approach written by Hajime Satō and published by American Mathematical Soc.. This book was released on 1999 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject. The purpose of this book is to help the aspiring reader acquire this essential common sense about algebraic topology in a short period of time. To this end, Sato leads the reader through simple but meaningful examples in concrete terms. Moreover, results are not discussed in their greatest possible generality, but in terms of the simplest and most essential cases. In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references. Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Möbius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles.

Topological Phases of Matter

Author : Roderich Moessner
Publisher : Cambridge University Press
ISBN 13 : 1107105536
Total Pages : 393 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Topological Phases of Matter by : Roderich Moessner

Download or read book Topological Phases of Matter written by Roderich Moessner and published by Cambridge University Press. This book was released on 2021-04-29 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.

The Topological Imagination

Author : Angus Fletcher
Publisher : Harvard University Press
ISBN 13 : 0674968867
Total Pages : 327 pages
Book Rating : 4.6/5 (749 download)

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Book Synopsis The Topological Imagination by : Angus Fletcher

Download or read book The Topological Imagination written by Angus Fletcher and published by Harvard University Press. This book was released on 2016-04-04 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boldly original and boundary defining, The Topological Imagination clears a space for an intellectual encounter with the shape of human imagining. Joining two commonly opposed domains, literature and mathematics, Angus Fletcher maps the imagination’s ever-ramifying contours and dimensions, and along the way compels us to re-envision our human existence on the most unusual sphere ever imagined, Earth. Words and numbers are the twin powers that create value in our world. Poetry and other forms of creative literature stretch our ability to evaluate through the use of metaphors. In this sense, the literary imagination aligns with topology, the branch of mathematics that studies shape and space. Topology grasps the quality of geometries rather than their quantifiable measurements. It envisions how shapes can be bent, twisted, or stretched without losing contact with their original forms—one of the discoveries of the eighteenth-century mathematician Leonhard Euler, whose Polyhedron Theorem demonstrated how shapes preserve “permanence in change,” like an aging though familiar face. The mysterious dimensionality of our existence, Fletcher says, is connected to our inhabiting a world that also inhabits us. Theories of cyclical history reflect circulatory biological patterns; the day-night cycle shapes our adaptive, emergent patterns of thought; the topology of islands shapes the evolution of evolutionary theory. Connecting literature, philosophy, mathematics, and science, The Topological Imagination is an urgent and transformative work, and a profound invitation to thought.