Topology And Maps

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Topology and Maps

Author : T. Husain
Publisher : Springer Science & Business Media
ISBN 13 : 1461587980
Total Pages : 347 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Topology and Maps by : T. Husain

Download or read book Topology and Maps written by T. Husain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is suitable for undergraduate students as well as advanced students and research workers. It consists of ten chapters, the first six of which are meant for beginners and are therefore suitable for undergraduate students; Chapters VII-X are suitable for advanced students and research workers interested in functional analysis. This book has two special features: First, it contains generalizations of continuous maps on topological spaces, e. g. , almost continuous maps, nearly continuous maps, maps with closed graph, graphically continuous maps, w-continuous maps, and a-continuous maps, etc. and some of their properties. The treatment of these notions appears here, in Chapter VII, for the first time in book form. The second feature consists in some not-so-easily-available nuptial delights that grew out of the marriage of topology and functional analysis; they are topics mainly courted by functional analysts and seldom given in topology books. Specifically, one knows that the set C(X) of all real- or com plex-valued continuous functions on a completely regular space X forms a locally convex topological algebra, a fortiori a topological vector space, in the compact-open topology. A number of theorems are known: For example, C(X) is a Banach space iff X is compact, or C(X) is complete iff X is a kr-space, and so on. Chapters VIII and X include this material, which, to the regret of many interested readers has not previously been available in book form (a recent publication (Weir [\06]) does, however, contain some material of our Chapter X).

Explorations in Topology

Author : David Gay
Publisher : Elsevier
ISBN 13 : 0124166407
Total Pages : 332 pages
Book Rating : 4.1/5 (241 download)

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Book Synopsis Explorations in Topology by : David Gay

Download or read book Explorations in Topology written by David Gay and published by Elsevier. This book was released on 2013-12-04 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised end-of-chapter notes provide historical background to the chapter's ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology. Students begin to solve substantial problems from the start Ideas unfold through the context of a storyline, and students become actively involved The text models the problem-solving process, presents the development of concepts in a natural way, and helps the reader engage with the material

Differential Topology

Author : Morris W. Hirsch
Publisher : Springer Science & Business Media
ISBN 13 : 146849449X
Total Pages : 230 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Differential Topology by : Morris W. Hirsch

Download or read book Differential Topology written by Morris W. Hirsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS

Topology of Singular Fibers of Differentiable Maps

Author : Osamu Saeki
Publisher : Springer
ISBN 13 : 3540446486
Total Pages : 154 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Topology of Singular Fibers of Differentiable Maps by : Osamu Saeki

Download or read book Topology of Singular Fibers of Differentiable Maps written by Osamu Saeki and published by Springer. This book was released on 2004-08-30 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.

Computational Topology for Data Analysis

Author : Tamal Krishna Dey
Publisher : Cambridge University Press
ISBN 13 : 1009103199
Total Pages : 456 pages
Book Rating : 4.0/5 (91 download)

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Book Synopsis Computational Topology for Data Analysis by : Tamal Krishna Dey

Download or read book Computational Topology for Data Analysis written by Tamal Krishna Dey and published by Cambridge University Press. This book was released on 2022-03-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.

Experiments in Topology

Author : Stephen Barr
Publisher : Courier Corporation
ISBN 13 : 048615274X
Total Pages : 244 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Experiments in Topology by : Stephen Barr

Download or read book Experiments in Topology written by Stephen Barr and published by Courier Corporation. This book was released on 2012-12-04 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.

Complements of Discriminants of Smooth Maps

Author : V. A. Vasilʹev
Publisher : American Mathematical Soc.
ISBN 13 : 9780821898376
Total Pages : 282 pages
Book Rating : 4.8/5 (983 download)

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Book Synopsis Complements of Discriminants of Smooth Maps by : V. A. Vasilʹev

Download or read book Complements of Discriminants of Smooth Maps written by V. A. Vasilʹev and published by American Mathematical Soc.. This book was released on 1994 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Up-to-date reference on this exciting area of mathematics * Discusses the wide range of applications in topology, algebraic geometry, and catastrophe theory.

Maps and the Internet

Author : M.P. Peterson
Publisher : Elsevier
ISBN 13 : 9780080449449
Total Pages : 474 pages
Book Rating : 4.4/5 (494 download)

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Book Synopsis Maps and the Internet by : M.P. Peterson

Download or read book Maps and the Internet written by M.P. Peterson and published by Elsevier. This book was released on 2005-12-17 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines a new trend affecting cartography and geographic information science. Presenting the work of over 30 authors from 16 different countries, the book provides an overview of current research in the new area of Internet Cartography. Chapters deal with the growth of this form of map distribution, uses in education, privacy issues, and technical aspects from the point of view of the map provider - including Internet protocols such as XML and SVG. Many see the Internet as a revolution for cartography. Previously tied to the medium of paper and expensive large-format color print technology, maps had a limited distribution and use. The Internet made it possible to not only distribute maps to a much larger audience but also to incorporate interaction and animation in the display. Maps have also become timelier with some maps of traffic and weather being updated every few minutes. In addition, it is now possible to access maps from servers throughout the world. Finally, the Internet has made historic maps available for viewing to the public that were previously only available in map libraries with limited access. * Provides comprehensive coverage of maps and the internet * Delivers a global perspective * Combines theoretical and practical aspects

Topology from the Differentiable Viewpoint

Author : John Willard Milnor
Publisher : Princeton University Press
ISBN 13 : 9780691048338
Total Pages : 80 pages
Book Rating : 4.0/5 (483 download)

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Book Synopsis Topology from the Differentiable Viewpoint by : John Willard Milnor

Download or read book Topology from the Differentiable Viewpoint written by John Willard Milnor and published by Princeton University Press. This book was released on 1997-12-14 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.

New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-novikov Theory

Author : Dan Burghelea
Publisher : World Scientific
ISBN 13 : 9814618268
Total Pages : 260 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-novikov Theory by : Dan Burghelea

Download or read book New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-novikov Theory written by Dan Burghelea and published by World Scientific. This book was released on 2017-08-16 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about new topological invariants of real- and angle-valued maps inspired by Morse-Novikov theory, a chapter of topology, which has recently raised interest outside of mathematics; for example, in data analysis, shape recognition, computer science and physics. They are the backbone of what the author proposes as a computational alternative to Morse-Novikov theory, referred to in this book as AMN-theory.These invariants are on one side analogues of rest points, instantons and closed trajectories of vector fields and on the other side, refine basic topological invariants like homology and monodromy. They are associated to tame maps, considerably more general than Morse maps, that are defined on spaces which are considerably more general than manifolds. They are computable by computer implementable algorithms and have strong robustness properties. They relate the dynamics of flows that admit the map as 'Lyapunov map' to the topology of the underlying space, in a similar manner as Morse-Novikov theory does.

Grassmannians and Gauss Maps in Piecewise-Linear Topology

Author : Norman Levitt
Publisher : Springer
ISBN 13 : 3540460780
Total Pages : 208 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Grassmannians and Gauss Maps in Piecewise-Linear Topology by : Norman Levitt

Download or read book Grassmannians and Gauss Maps in Piecewise-Linear Topology written by Norman Levitt and published by Springer. This book was released on 2006-11-14 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores the possibility of extending the notions of "Grassmannian" and "Gauss map" to the PL category. They are distinguished from "classifying space" and "classifying map" which are essentially homotopy-theoretic notions. The analogs of Grassmannian and Gauss map defined incorporate geometric and combinatorial information. Principal applications involve characteristic class theory, smoothing theory, and the existence of immersion satifying certain geometric criteria, e.g. curvature conditions. The book assumes knowledge of basic differential topology and bundle theory, including Hirsch-Gromov-Phillips theory, as well as the analogous theories for the PL category. The work should be of interest to mathematicians concerned with geometric topology, PL and PD aspects of differential geometry and the geometry of polyhedra.

Introduction to Topological Manifolds

Author : John M. Lee
Publisher : Springer Science & Business Media
ISBN 13 : 038722727X
Total Pages : 395 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Introduction to Topological Manifolds by : John M. Lee

Download or read book Introduction to Topological Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.

Topology and Approximate Fixed Points

Author : Afif Ben Amar
Publisher : Springer Nature
ISBN 13 : 3030922049
Total Pages : 258 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Topology and Approximate Fixed Points by : Afif Ben Amar

Download or read book Topology and Approximate Fixed Points written by Afif Ben Amar and published by Springer Nature. This book was released on 2022-01-25 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory. This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces—and fundamental properties of their topologies—are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included are weak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak* topology of its dual, and the Fréchet-Urysohn property. The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies. By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed point theory.

Basic Topology

Author : M.A. Armstrong
Publisher : Springer Science & Business Media
ISBN 13 : 1475717938
Total Pages : 260 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Basic Topology by : M.A. Armstrong

Download or read book Basic Topology written by M.A. Armstrong and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties help students gain a thorough understanding of the subject.

Differential Topology

Author : J. Margalef-Roig
Publisher : Elsevier
ISBN 13 : 0444884343
Total Pages : 622 pages
Book Rating : 4.4/5 (448 download)

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Book Synopsis Differential Topology by : J. Margalef-Roig

Download or read book Differential Topology written by J. Margalef-Roig and published by Elsevier. This book was released on 1992-06-02 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: ...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor

A Geometric Introduction to Topology

Author : Charles Terence Clegg Wall
Publisher : Courier Corporation
ISBN 13 : 0486678504
Total Pages : 195 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis A Geometric Introduction to Topology by : Charles Terence Clegg Wall

Download or read book A Geometric Introduction to Topology written by Charles Terence Clegg Wall and published by Courier Corporation. This book was released on 1993-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: First course in algebraic topology for advanced undergraduates. Homotopy theory, the duality theorem, relation of topological ideas to other branches of pure mathematics. Exercises and problems. 1972 edition.

Topology Through Inquiry

Author : Michael Starbird
Publisher : American Mathematical Soc.
ISBN 13 : 1470462613
Total Pages : 313 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topology Through Inquiry by : Michael Starbird

Download or read book Topology Through Inquiry written by Michael Starbird and published by American Mathematical Soc.. This book was released on 2020-09-10 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.