Understanding Topology

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Understanding Topology

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Author : Shaun V. Ault
language : en
Publisher: JHU Press
Release Date : 2018-01-30

Understanding Topology written by Shaun V. Ault and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Mathematics categories.

"Topology can present significant challenges for undergraduate students of mathematics and the sciences. 'Understanding topology' aims to change that. The perfect introductory topology textbook, 'Understanding topology' requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from chemical dynamics to determining the shape of the universe, will engage students in a way traditional topology textbooks do not"--Back cover.

Understanding Cisco Networking Technologies Volume 1

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Author : Todd Lammle
language : en
Publisher: John Wiley & Sons
Release Date : 2019-12-24

Understanding Cisco Networking Technologies Volume 1 written by Todd Lammle and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-24 with Computers categories.

Leading Cisco authority Todd Lammle helps you gain insights into the new core Cisco network technologies Understanding Cisco Networking Technologies is an important resource for those preparing for the new Cisco Certified Network Associate (CCNA) certification exam as well as IT professionals looking to understand Cisco’s latest networking products, services, and technologies. Written by bestselling author and internationally recognized Cisco expert Todd Lammle, this in-depth guide provides the fundamental knowledge required to implement and administer a broad range of modern networking and IT infrastructure. Cisco is the worldwide leader in network technologies—80% of the routers on the Internet are Cisco. This authoritative book provides you with a solid foundation in Cisco networking, enabling you to apply your technical knowledge to real-world tasks. Clear and accurate chapters cover topics including routers, switches, controllers and other network components, physical interface and cabling, IPv6 addressing, discovery protocols, wireless infrastructure, security features and encryption protocols, controller-based and software-defined architectures, and more. After reading this essential guide, you will understand: Network fundamentals Network access IP connectivity and IP services Security fundamentals Automation and programmability Understanding Cisco Networking Technologies is a must-read for anyone preparing for the new CCNA certification or looking to gain a primary understanding of key Cisco networking technologies.

Topology For Computing

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Author : Afra J. Zomorodian
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-10

Topology For Computing written by Afra J. Zomorodian and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-10 with Computers categories.

The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.

Understanding Imagination

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Author : Dennis L Sepper
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-13

Understanding Imagination written by Dennis L Sepper 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 2013-05-13 with Science categories.

This book discusses that imagination is as important to thinking and reasoning as it is to making and acting. By reexamining our philosophical and psychological heritage, it traces a framework, a conceptual topology, that underlies the most disparate theories: a framework that presents imagination as founded in the placement of appearances. It shows how this framework was progressively developed by thinkers like Plato, Aristotle, Descartes, and Kant, and how it is reflected in more recent developments in theorists as different as Peirce, Saussure, Wittgenstein, Benjamin, and Bachelard. The conceptual topology of imagination incorporates logic, mathematics, and science as well as production, play, and art. Recognizing this topology can move us past the confusions to a unifying view of imagination for the future. ​

Introduction To Topology

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Author : Bert Mendelson
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26

Introduction To Topology written by Bert Mendelson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.

Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

Topology Unravelling The Fabric Of Space

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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-04-20

Topology Unravelling The Fabric Of Space written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-20 with Mathematics categories.

Embark on a captivating journey through the world of topology with Topology: Unravelling the Fabric of Space, a comprehensive guide that unveils the intricate beauty and profound insights of this fascinating mathematical discipline. Discover how topology unravels the fabric of space, providing a framework for understanding the structure of our universe and beyond. Delve into the fundamental concepts of topology, exploring the properties of geometric figures that remain unchanged under continuous deformations. Uncover the significance of topological spaces, homeomorphisms, and homology, and witness how these concepts lay the foundation for understanding the structure and behavior of shapes and spaces. Explore the realm of topological invariants, numerical measures that capture the essence of geometric objects. Learn how these invariants enable mathematicians to classify and compare different shapes and spaces, providing deep insights into their underlying structure. Discover the applications of topological invariants in diverse fields, from physics and engineering to computer science and biology. Witness the power of topology in unraveling the mysteries of the physical world. Delve into the geometry of spacetime, the fundamental fabric of our universe, and understand how topology provides insights into the behavior of elementary particles, the structure of atoms, and the properties of black holes. Discover the profound impact of topology on computer science, where it finds applications in computer graphics, image processing, and network analysis. Explore how topological algorithms efficiently represent and manipulate complex data structures, optimize routing protocols, and design efficient algorithms for solving computational problems. Topology: Unravelling the Fabric of Space is an indispensable resource for students, researchers, and anyone fascinated by the intricate world of shapes and spaces. Its comprehensive coverage of fundamental concepts, theorems, and applications makes it an invaluable guide to the captivating realm of topology. If you like this book, write a review on google books!

Geometry And Topological Concepts

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Author : Dr. P. Somashekhara
language : en
Publisher: RK Publication
Release Date : 2024-09-21

Geometry And Topological Concepts written by Dr. P. Somashekhara and has been published by RK Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-21 with Juvenile Nonfiction categories.

Geometry and Topological Concepts is an exploration of the fundamental principles and applications of geometry and topology in mathematics and related fields. This book delves into the intricacies of shapes, sizes, and the properties of space, emphasizing the connections between these areas of study. It covers essential topics such as Euclidean and non-Euclidean geometries, topological spaces, and geometric transformations, providing readers with both theoretical foundations and practical examples. Ideal for students and professionals, it fosters a deeper understanding of the mathematical structures that underpin our world.

Point Set Topology

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Author : Steven A. Gaal
language : en
Publisher: Courier Corporation
Release Date : 2009-04-23

Point Set Topology written by Steven A. Gaal and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-23 with Mathematics categories.

Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.

Geometric Aspects Of General Topology

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Author : Katsuro Sakai
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-22

Geometric Aspects Of General Topology written by Katsuro Sakai 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 2013-07-22 with Mathematics categories.

This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars. Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim X × I = dim X + 1 for a metrizable space X; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomological dimension; a dimension raising cell-like map; and a non-AR metric linear space. The final chapter enables students to understand how deeply related the two theories are. Simplicial complexes are very useful in topology and are indispensable for studying the theories of both dimension and ANRs. There are many textbooks from which some knowledge of these subjects can be obtained, but no textbook discusses non-locally finite simplicial complexes in detail. So, when we encounter them, we have to refer to the original papers. For instance, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any textbook. The homotopy type of simplicial complexes is discussed in textbooks on algebraic topology using CW complexes, but geometrical arguments using simplicial complexes are rather easy.

Topology

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Author : Tai-Danae Bradley
language : en
Publisher: MIT Press
Release Date : 2020-08-18

Topology written by Tai-Danae Bradley and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-18 with Mathematics categories.

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. After presenting the basics of both category theory and topology, the book covers the universal properties of familiar constructions and three main topological properties—connectedness, Hausdorff, and compactness. It presents a fine-grained approach to convergence of sequences and filters; explores categorical limits and colimits, with examples; looks in detail at adjunctions in topology, particularly in mapping spaces; and examines additional adjunctions, presenting ideas from homotopy theory, the fundamental groupoid, and the Seifert van Kampen theorem. End-of-chapter exercises allow students to apply what they have learned. The book expertly guides students of topology through the important transition from undergraduate student with a solid background in analysis or point-set topology to graduate student preparing to work on contemporary problems in mathematics.