Topology And Its Applications

Author : William F. Basener
Publisher : John Wiley & Sons
Page : 295 pages
File Size : 42,8 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781118626221

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Topology and Its Applications by William F. Basener Pdf

Discover a unique and modern treatment of topology employing a cross-disciplinary approach Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical field that highlights mathematical theory to a subject that plays a growing role in nearly all fields of scientific investigation. Moving from the concrete to the abstract, Topology and Its Applications displays both the beauty and utility of topology, first presenting the essentials of topology followed by its emerging role within the new frontiers in research. Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs. This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation. The author presents a diversity of topological areas, including point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. Topics within these areas include: Open sets Compactness Homotopy Surface classification Index theory on surfaces Manifolds and complexes Topological groups The fundamental group and homology Special "core intuition" segments throughout the book briefly explain the basic intuition essential to understanding several topics. A generous number of figures and examples, many of which come from applications such as liquid crystals, space probe data, and computer graphics, are all available from the publisher's Web site.

Author : Ulrich Höhle
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 49,6 Mb
Release : 2001-04-30
Category : Mathematics
ISBN : 0792373189

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Many Valued Topology and its Applications by Ulrich Höhle Pdf

The 20th Century brought the rise of General Topology. It arose from the effort to establish a solid base for Analysis and it is intimately related to the success of set theory. Many Valued Topology and Its Applications seeks to extend the field by taking the monadic axioms of general topology seriously and continuing the theory of topological spaces as topological space objects within an almost completely ordered monad in a given base category C. The richness of this theory is shown by the fundamental fact that the category of topological space objects in a complete and cocomplete (epi, extremal mono)-category C is topological over C in the sense of J. Adamek, H. Herrlich, and G.E. Strecker. Moreover, a careful, categorical study of the most important topological notions and concepts is given - e.g., density, closedness of extremal subobjects, Hausdorff's separation axiom, regularity, and compactness. An interpretation of these structures, not only by the ordinary filter monad, but also by many valued filter monads, underlines the richness of the explained theory and gives rise to new concrete concepts of topological spaces - so-called many valued topological spaces. Hence, many valued topological spaces play a significant role in various fields of mathematics - e.g., in the theory of locales, convergence spaces, stochastic processes, and smooth Borel probability measures. In its first part, the book develops the necessary categorical basis for general topology. In the second part, the previously given categorical concepts are applied to monadic settings determined by many valued filter monads. The third part comprises various applications of many valued topologies to probability theory and statistics as well as to non-classical model theory. These applications illustrate the significance of many valued topology for further research work in these important fields.

Author : J. van Mill,George M. Reed
Publisher : North Holland
Page : 716 pages
File Size : 43,6 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015018940943

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Open Problems in Topology by J. van Mill,George M. Reed Pdf

From the Introduction: This volume grew from a discussion by the editors on the difficulty of finding good thesis problems for graduate students in topology. Although at any given time we each had our own favorite problems, we acknowledged the need to offer students a wider selection from which to choose a topic peculiar to their interests. One of us remarked, 'Wouldn't it be nice to have a book of current unsolved problems always available to pull down from the shelf?' The other replied 'Why don't we simply produce such a book?' Two years later and not so simply, here is the resulting volume. The intent is to provide not only a source book for thesis-level problems but also a challenge to the best researchers in the field.

Author : Mahima Ranjan Adhikari
Publisher : Springer
Page : 615 pages
File Size : 42,8 Mb
Release : 2016-09-16
Category : Mathematics
ISBN : 9788132228431

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Basic Algebraic Topology and its Applications by Mahima Ranjan Adhikari Pdf

This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Author : Steven G. Krantz
Publisher : CRC Press
Page : 422 pages
File Size : 40,9 Mb
Release : 2009-07-28
Category : Mathematics
ISBN : 9781420089752

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Essentials of Topology with Applications by Steven G. Krantz Pdf

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

Author : Somashekhar A. Naimpally,James F. Peters
Publisher : World Scientific
Page : 294 pages
File Size : 46,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814407663

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Topology with Applications by Somashekhar A. Naimpally,James F. Peters Pdf

The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.

Author : Sergeĭ Petrovich Novikov
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 51,6 Mb
Release : 1993
Category : Mathematics
ISBN : 0821831518

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Topology and Its Applications by Sergeĭ Petrovich Novikov Pdf

The Proceedings of an international topology conference - this book covrs various aspects of general algebraic, and low-dimensional topology.

Author : P. A. Firby,Cyril F. Gardiner
Publisher : Halsted Press
Page : 224 pages
File Size : 50,8 Mb
Release : 1982
Category : Mathematics
ISBN : UOM:39015015610564

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Surface Topology by P. A. Firby,Cyril F. Gardiner Pdf

Author : Jonathan A. Barmak
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 42,5 Mb
Release : 2011-08-24
Category : Mathematics
ISBN : 9783642220029

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Algebraic Topology of Finite Topological Spaces and Applications by Jonathan A. Barmak Pdf

This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.

Author : S. Lefschetz
Publisher : Springer Science & Business Media
Page : 190 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493672

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Applications of Algebraic Topology by S. Lefschetz Pdf

This monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge of linear algebra and of topology. In topology the limit is dimension two mainly in the latter chapters and questions of topological invariance are carefully avoided. From the technical viewpoint graphs is our only requirement. However, later, questions notably related to Kuratowski's classical theorem have demanded an easily provided treatment of 2-complexes and surfaces. January 1972 Solomon Lefschetz 4 INTRODUCTION The study of electrical networks rests upon preliminary theory of graphs. In the literature this theory has always been dealt with by special ad hoc methods. My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. Part I of this volume covers the following ground: The first two chapters present, mainly in outline, the needed basic elements of linear algebra. In this part duality is dealt with somewhat more extensively. In Chapter III the merest elements of general topology are discussed. Graph theory proper is covered in Chapters IV and v, first structurally and then as algebra. Chapter VI discusses the applications to networks. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.

Author : Gunnar E. Carlsson,Ralph L. Cohen,Wu-Chung Hsiang,John D.S. Jones
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461395263

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Algebraic Topology and Its Applications by Gunnar E. Carlsson,Ralph L. Cohen,Wu-Chung Hsiang,John D.S. Jones Pdf

In 1989-90 the Mathematical Sciences Research Institute conducted a program on Algebraic Topology and its Applications. The main areas of concentration were homotopy theory, K-theory, and applications to geometric topology, gauge theory, and moduli spaces. Workshops were conducted in these three areas. This volume consists of invited, expository articles on the topics studied during this program. They describe recent advances and point to possible new directions. They should prove to be useful references for researchers in Algebraic Topology and related fields, as well as to graduate students.

Author : Elliott M. Pearl
Publisher : Elsevier
Page : 776 pages
File Size : 54,8 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 0080475299

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Open Problems in Topology II by Elliott M. Pearl Pdf

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

Author : S.P. Novikov,A.T. Fomenko
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 41,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401578950

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Basic Elements of Differential Geometry and Topology by S.P. Novikov,A.T. Fomenko Pdf

One service mathematics has rendered the 'Et moi ..., si j'avait su comment en revenir, je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Matht"natics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics seNe as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series

Author : Erica Flapan
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 54,5 Mb
Release : 2015-12-22
Category : Algebraic topology
ISBN : 9781470425357

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Knots, Molecules, and the Universe by Erica Flapan Pdf

This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook. The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material. The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details.

Author : Muhammad Riaz ,Masooma Raza Hashmi
Publisher : Infinite Study
Page : 22 pages
File Size : 54,9 Mb
Release : 2024-06-15
Category : Mathematics
ISBN : 8210379456XXX

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m-polar Neutrosophic Topology and its Application to Medical Diagnosis by Muhammad Riaz ,Masooma Raza Hashmi Pdf

In the present study we aim to introduce novel concepts of m-polar neutrosophic set (MPNS) and m-polar neutrosophic topology. For this aim, we first investigate several characterizations of the notion of m-polar neutrosophic set and discuss its fundamental properties. We establish some operations on m-polar neutrosophic set. We propose score functions for the comparison of m-polar neutrosophic numbers (MPNNs). Then we introduce m-polar neutrosophic topology and define interior, closure, exterior and frontier for m-polar neutrosophic sets (MPNSs) with illustrative examples. We discuss some results which holds for classical set theory but do not hold for m-polar neutrosophic set theory. We introduce cosine similarity measure and set theoretic similarity measures for MPNSs. Furthermore, we present two algorithms for multi-criteria decision-making (MCDM) in medical diagnosis by using m-polar neutrosophic set (MPNS) and m-polar neutrosophic topology.