Topological Structures Ii

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Topological Groups and Related Structures, An Introduction to Topological Algebra.

Author : Alexander Arhangel’skii
Publisher : Springer Science & Business Media
ISBN 13 : 949121635X
Total Pages : 794 pages
Book Rating : 4.4/5 (912 download)

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Book Synopsis Topological Groups and Related Structures, An Introduction to Topological Algebra. by : Alexander Arhangel’skii

Download or read book Topological Groups and Related Structures, An Introduction to Topological Algebra. written by Alexander Arhangel’skii and published by Springer Science & Business Media. This book was released on 2008-05-01 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.

Basic Topological Structures of Ordinary Differential Equations

Author : V.V. Filippov
Publisher : Springer Science & Business Media
ISBN 13 : 940170841X
Total Pages : 536 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Basic Topological Structures of Ordinary Differential Equations by : V.V. Filippov

Download or read book Basic Topological Structures of Ordinary Differential Equations written by V.V. Filippov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is a detailed study of topological effects related to continuity of the dependence of solutions on initial values and parameters. This allows us to develop cheaply a theory which deals easily with equations having singularities and with equations with multivalued right hand sides (differential inclusions). An explicit description of corresponding topological structures expands the theory in the case of equations with continuous right hand sides also. In reality, this is a new science where Ordinary Differential Equations, General Topology, Integration theory and Functional Analysis meet. In what concerns equations with discontinuities and differential inclu sions, we do not restrict the consideration to the Cauchy problem, but we show how to develop an advanced theory whose volume is commensurable with the volume of the existing theory of Ordinary Differential Equations. The level of the account rises in the book step by step from second year student to working scientist.

Elements of Operator Theory

Author : Carlos S. Kubrusly
Publisher : Springer Science & Business Media
ISBN 13 : 1475733283
Total Pages : 535 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Elements of Operator Theory by : Carlos S. Kubrusly

Download or read book Elements of Operator Theory written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: {\it Elements of Operatory Theory} is aimed at graduate students as well as a new generation of mathematicians and scientists who need to apply operator theory to their field. Written in a user-friendly, motivating style, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, Hilbert spaces, culminating with the Spectral Theorem, one of the landmarks in the theory of operators on Hilbert spaces. The exposition is concept-driven and as much as possible avoids the formula-computational approach. Key features of this largely self-contained work include: * required background material to each chapter * fully rigorous proofs, over 300 of them, are specially tailored to the presentation and some are new * more than 100 examples and, in several cases, interesting counterexamples that demonstrate the frontiers of an important theorem * over 300 problems, many with hints * both problems and examples underscore further auxiliary results and extensions of the main theory; in this non-traditional framework, the reader is challenged and has a chance to prove the principal theorems anew This work is an excellent text for the classroom as well as a self-study resource for researchers. Prerequisites include an introduction to analysis and to functions of a complex variable, which most first-year graduate students in mathematics, engineering, or another formal science have already acquired. Measure theory and integration theory are required only for the last section of the final chapter.

New Foundations for Physical Geometry

Author : Tim Maudlin
Publisher :
ISBN 13 : 0198701306
Total Pages : 374 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis New Foundations for Physical Geometry by : Tim Maudlin

Download or read book New Foundations for Physical Geometry written by Tim Maudlin and published by . This book was released on 2014-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.

A Short Course on Topological Insulators

Author : János K. Asbóth
Publisher : Springer
ISBN 13 : 3319256076
Total Pages : 176 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis A Short Course on Topological Insulators by : János K. Asbóth

Download or read book A Short Course on Topological Insulators written by János K. Asbóth and published by Springer. This book was released on 2016-02-22 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.

Topological Uniform Structures

Author : Warren Page
Publisher : Courier Dover Publications
ISBN 13 : 9780486658087
Total Pages : 398 pages
Book Rating : 4.6/5 (58 download)

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Book Synopsis Topological Uniform Structures by : Warren Page

Download or read book Topological Uniform Structures written by Warren Page and published by Courier Dover Publications. This book was released on 1988 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exceptionally smooth, clear, detailed examination of uniform spaces, topological groups, topological vector spaces, topological algebras and abstract harmonic analysis. Also, topological vector-valued measure spaces as well as numerous problems and examples. For advanced undergraduates and beginning graduate students. Bibliography. Index.

Coarse Geometry of Topological Groups

Author : Christian Rosendal
Publisher : Cambridge University Press
ISBN 13 : 110884247X
Total Pages : 309 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Coarse Geometry of Topological Groups by : Christian Rosendal

Download or read book Coarse Geometry of Topological Groups written by Christian Rosendal and published by Cambridge University Press. This book was released on 2021-12-16 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.

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.

Topological Structures in Ferroic Materials

Author : Jan Seidel
Publisher : Springer
ISBN 13 : 3319253018
Total Pages : 249 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Topological Structures in Ferroic Materials by : Jan Seidel

Download or read book Topological Structures in Ferroic Materials written by Jan Seidel and published by Springer. This book was released on 2016-02-12 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a state-of-the art overview of a highly interesting emerging research field in solid state physics/nanomaterials science, topological structures in ferroic materials. Topological structures in ferroic materials have received strongly increasing attention in the last few years. Such structures include domain walls, skyrmions and vortices, which can form in ferroelectric, magnetic, ferroelastic or multiferroic materials. These topological structures can have completely different properties from the bulk material they form in. They also can be controlled by external fields (electrical, magnetic, strain) or currents, which makes them interesting from a fundamental research point of view as well as for potential novel nanomaterials applications. To provide a comprehensive overview, international leading researches in these fields contributed review-like chapters about their own work and the work of other researchers to provide a current view of this highly interesting topic.

Recent Progress in General Topology II

Author : M. Husek
Publisher : Elsevier
ISBN 13 : 0080929958
Total Pages : 651 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Recent Progress in General Topology II by : M. Husek

Download or read book Recent Progress in General Topology II written by M. Husek and published by Elsevier. This book was released on 2002-11-13 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents surveys describing recent developments in most of the primary subfields ofGeneral Topology and its applications to Algebra and Analysis during the last decade. It follows freelythe previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared inconnection with the Prague Topological Symposium, held in 2001. During the last 10 years the focusin General Topology changed and therefore the selection of topics differs slightly from thosechosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (includingInfinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as:R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.

Topological Data Structures for Surfaces

Author : Sanjay Rana
Publisher : John Wiley & Sons
ISBN 13 : 9780470851517
Total Pages : 222 pages
Book Rating : 4.8/5 (515 download)

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Book Synopsis Topological Data Structures for Surfaces by : Sanjay Rana

Download or read book Topological Data Structures for Surfaces written by Sanjay Rana and published by John Wiley & Sons. This book was released on 2004-05-21 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Geography and GIS, surfaces can be analysed and visualised through various data structures, and topological data structures describe surfaces in the form of a relationship between certain surface-specific features. Drawn from many disciplines with a strong applied aspect, this is a research-led, interdisciplinary approach to the creation, analysis and visualisation of surfaces, focussing on topological data structures. Topological Data Structures for Surfaces: an introduction for Geographical Information Science describes the concepts and applications of these data structures. The book focuses on how these data structures can be used to analyse and visualise surface datasets from a range of disciplines such as human geography, computer graphics, metrology, and physical geography. Divided into two Parts, Part I defines the topological surface data structures and explains the various automated methods used for their generation. Part II demonstrates a number of applications of surface networks in diverse fields, ranging from sub-atomic particle collision visualisation to the study of population density patterns. To ensure that the material is accessible, each Part is prefaced by an overview of the techniques and application. Provides GI scientists and geographers with an accessible overview of current surface topology research. Algorithms are presented and explained with practical examples of their usage. Features an accompanying website developed by the Editor - http://geog.le.ac.uk/sanjayrana/surface-networks/ This book is invaluable for researchers and postgraduate students working in departments of GI Science, Geography and Computer Science. It also constitutes key reference material for Masters students working on surface analysis projects as part of a GI Science or Computer Science programme.

Davenport-Schinzel Sequences and Their Geometric Applications

Author : Micha Sharir
Publisher : Cambridge University Press
ISBN 13 : 9780521470254
Total Pages : 388 pages
Book Rating : 4.4/5 (72 download)

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Book Synopsis Davenport-Schinzel Sequences and Their Geometric Applications by : Micha Sharir

Download or read book Davenport-Schinzel Sequences and Their Geometric Applications written by Micha Sharir and published by Cambridge University Press. This book was released on 1995-05-26 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive treatment of a fundamental tool for solving problems in computational and combinatorial geometry.

Analytic Topology

Author : Gordon Thomas Whyburn
Publisher : American Mathematical Soc.
ISBN 13 : 0821810286
Total Pages : 295 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Analytic Topology by : Gordon Thomas Whyburn

Download or read book Analytic Topology written by Gordon Thomas Whyburn and published by American Mathematical Soc.. This book was released on 1963 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The material here presented represents an elaboration on my Colloquium Lectures delivered before the American Mathematical Society at its September, 1940 meeting at Dartmouth College." - Preface.

Open Problems in Topology II

Author : Elliott M. Pearl
Publisher : Elsevier
ISBN 13 : 0080475299
Total Pages : 777 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Open Problems in Topology II by : Elliott M. Pearl

Download or read book Open Problems in Topology II written by Elliott M. Pearl and published by Elsevier. This book was released on 2011-08-11 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis.* New surveys of research problems in topology* New perspectives on classic problems* Representative surveys of research groups from all around the world

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.

From Differential Geometry to Non-commutative Geometry and Topology

Author : Neculai S. Teleman
Publisher : Springer Nature
ISBN 13 : 3030284336
Total Pages : 406 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis From Differential Geometry to Non-commutative Geometry and Topology by : Neculai S. Teleman

Download or read book From Differential Geometry to Non-commutative Geometry and Topology written by Neculai S. Teleman and published by Springer Nature. This book was released on 2019-11-10 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.

Elementary Concepts of Topology

Author : Paul Alexandroff
Publisher : Courier Corporation
ISBN 13 : 0486155064
Total Pages : 68 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Elementary Concepts of Topology by : Paul Alexandroff

Download or read book Elementary Concepts of Topology written by Paul Alexandroff and published by Courier Corporation. This book was released on 2012-08-13 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.