Geometric Aspects Of General Topology

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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 And Geometry

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Author : Glen E. Bredon
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-06-24

Topology And Geometry written by Glen E. Bredon 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 1993-06-24 with Education categories.

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS

General Topology I

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Author : A.V. Arkhangel'skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

General Topology I written by A.V. Arkhangel'skii 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 2012-12-06 with Mathematics categories.

This is the first of the encyclopaedia volumes devoted to general topology. It has two parts. The first outlines the basic concepts and constructions of general topology, including several topics which have not previously been covered in English language texts. The second part presents a survey of dimension theory, from the very beginnings to the most important recent developments. The principal ideas and methods are treated in detail, and the main results are provided with sketches of proofs. The authors have suceeded admirably in the difficult task of writing a book which will not only be accessible to the general scientist and the undergraduate, but will also appeal to the professional mathematician. The authors' efforts to detail the relationship between more specialized topics and the central themes of topology give the book a broad scholarly appeal which far transcends narrow disciplinary lines.

Recent Progress In General Topology Iii

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Author : K.P. Hart
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11

Recent Progress In General Topology Iii written by K.P. Hart 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 2013-12-11 with Mathematics categories.

The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

A Geometric Introduction To Topology

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Author : Charles Terence Clegg Wall
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1972

A Geometric Introduction To Topology written by Charles Terence Clegg Wall and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.

Geometric And Topological Inference

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Author : Jean-Daniel Boissonnat
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-27

Geometric And Topological Inference written by Jean-Daniel Boissonnat 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 2018-09-27 with Computers categories.

A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

Elements Of Point Set Topology

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Author : John D. Baum
language : en
Publisher: Courier Corporation
Release Date : 1991-01-01

Elements Of Point Set Topology written by John D. Baum and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.

Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

Geometric Aspects Of Probability Theory And Mathematical Statistics

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Author : V.V. Buldygin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Geometric Aspects Of Probability Theory And Mathematical Statistics written by V.V. Buldygin 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 2013-06-29 with Mathematics categories.

It is well known that contemporary mathematics includes many disci plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we have the following extensive chap ters: the theory of compact extensions of topological spaces, the theory of continuous mappings, cardinal-valued characteristics of topological spaces, the theory of set-valued (multi-valued) mappings, etc. Modern algebra is featured by the following domains: linear algebra, group theory, the theory of rings, universal algebras, lattice theory, category theory, and so on. Concerning modern probability theory, we can easily see that the clas sification of its domains is much more extensive: measure theory on ab stract spaces, Borel and cylindrical measures in infinite-dimensional vector spaces, classical limit theorems, ergodic theory, general stochastic processes, Markov processes, stochastical equations, mathematical statistics, informa tion theory and many others.

Geometric Aspects Of Banach Spaces

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Author : E. Martin-Peinador
language : en
Publisher: Cambridge University Press
Release Date : 1989-07-06

Geometric Aspects Of Banach Spaces written by E. Martin-Peinador 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 1989-07-06 with Mathematics categories.

This volume concentrates on some important and contemporary themes in Banach space theory.

Algebraic Topology An Intuitive Approach

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Author : Hajime Satō
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Algebraic Topology An Intuitive Approach written by Hajime Satō and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

Develops an introduction to algebraic topology mainly through simple examples built on cell complexes. Topics covers include homeomorphisms, topological spaces and cell complexes, homotopy, homology, cohomology, the universal coefficient theorem, fiber bundles and vector bundles, and spectral sequences. Includes chapter summaries, exercises, and answers. Includes an appendix of definitions in sets, topology, and groups. Originally published in Japanese by Iwanami Shoten, Publishers, Tokyo, 1996. Annotation copyrighted by Book News, Inc., Portland, OR