Principles Of Topology
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Principles Of Topology
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Author : Fred H. Croom
language : en
Publisher: Courier Dover Publications
Release Date : 2016-03-17
Principles Of Topology written by Fred H. Croom and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-17 with Mathematics categories.
Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract, the treatment emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. Customary topics of point-set topology include metric spaces, general topological spaces, continuity, topological equivalence, basis, subbasis, connectedness, compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces. In addition, the text introduces geometric, differential, and algebraic topology. Each chapter includes historical notes to put important developments into their historical framework. Exercises of varying degrees of difficulty form an essential part of the text.
Principles Of Topology Hardcover
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Author : Fred H. Croom
language : ko
Publisher:
Release Date : 2009-09-09
Principles Of Topology Hardcover written by Fred H. Croom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-09 with categories.
Variational Principles Of Topology
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Author : A.T. Fomenko
language : en
Publisher: Springer
Release Date : 1990-04-30
Variational Principles Of Topology written by A.T. Fomenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-04-30 with Mathematics categories.
One service mathematics has rendered the 'Eot moi, ... , si j'avait JU comment en revenir. human race. h has put common sense back je n'y serais point aUe:' Jules Verne where it belongs, 011 the topmost shelf nen to the dusty canister labeUed 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. H es viside Mathematics 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 serve as tools for other pans 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.
Principles Of Topological Psychology
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Author : Kurt Lewin
language : en
Publisher: Read Books Ltd
Release Date : 2013-04-16
Principles Of Topological Psychology written by Kurt Lewin and has been published by Read Books Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-16 with Psychology categories.
This antiquarian text contains a comprehensive treatise on topological psychology, being a detailed exposition of its principles written by Kurt Lewin. Written in clear, plain language and full of information fundamental to understanding this branch of psychology, this text will be of considerable utility to the student, and it would make for a great addition to collections of allied literature. The chapters of this book include: 'The Present State of Psychology', 'Formulation of Laws and Representations of General Situations', 'Considerations About Representing Life Space', 'Context and Extent of the Psychological Life Space', 'Causal Interconnections in Psychology', etcetera. We are republishing this vintage book now complete with a specially commissioned new biography of the author.
Topological Principles In Cartography
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Author : James P. Corbett
language : en
Publisher:
Release Date : 1979
Topological Principles In Cartography written by James P. Corbett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Cartography categories.
Mathematical Principles Of Topological And Geometric Data Analysis
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Author : Parvaneh Joharinad
language : en
Publisher:
Release Date : 2023
Mathematical Principles Of Topological And Geometric Data Analysis written by Parvaneh Joharinad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information. In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately. Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use.
Variational Principles Of Topology
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Author : A.T. Fomenko
language : en
Publisher: Springer
Release Date : 2011-10-05
Variational Principles Of Topology written by A.T. Fomenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-05 with Mathematics categories.
One service mathematics has rendered the 'Eot moi, ... , si j'avait JU comment en revenir. human race. h has put common sense back je n'y serais point aUe:' Jules Verne where it belongs, 011 the topmost shelf nen to the dusty canister labeUed 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. H es viside Mathematics 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 serve as tools for other pans 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.
Topological Fixed Point Principles For Boundary Value Problems
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Author : J. Andres
language : en
Publisher:
Release Date : 2014-01-15
Topological Fixed Point Principles For Boundary Value Problems written by J. Andres and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Topology For Analysis
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Author : Albert Wilansky
language : en
Publisher: Courier Corporation
Release Date : 2008-10-17
Topology For Analysis written by Albert Wilansky and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-17 with Mathematics categories.
Starting with the first principles of topology, this volume advances to general analysis. Three levels of examples and problems make it appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important concepts, and a 40-page appendix includes tables of theorems and counterexamples. 1970 edition.
Topology And Approximate Fixed Points
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Author : Afif Ben Amar
language : en
Publisher: Springer Nature
Release Date : 2022-01-25
Topology And Approximate Fixed Points written by Afif Ben Amar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-25 with Mathematics categories.
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.