Homological Features Of Rings Of Continuous Functions

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Ordered Algebraic Structures

Author : W.C. Holland
Publisher : Springer Science & Business Media
ISBN 13 : 9401156409
Total Pages : 334 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Ordered Algebraic Structures by : W.C. Holland

Download or read book Ordered Algebraic Structures written by W.C. Holland and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference on Ordered Algebraic Structures held in Curat;ao, from the 26th of June through the 30th of June, 1995, at the Avila Beach Hotel, marked the eighth year of ac tivities by the Caribbean Mathematics Foundation (abbr. CMF), which was the principal sponsor of this conference. CMF was inaugurated in 1988 with a conference on Ordered Algebraic Structures. During the years between these two conferences the field has changed sufficiently, both from my point of view and, I believe, that of my co-organizer, W. Charles Holland, to make one wonder about the label "Ordered Algebraic Structures" itself. We recognized this from the start, and right away this conference carried a subtitle, or, if one prefers, an agenda: we concentrated on the one hand, on traditional themes in the theory of ordered groups, including model-theoretic aspects, and, on the other hand, on matters in which topology (more precisely C(X)-style topology) and category theory would play a prominent role. Plainly, ordered algebra has many faces, and it is becoming increas ingly difficult to organize an intimate conference, such as the ones encouraged in the series sponsored by CMF, in this area on a broad set of themes. These proceedings reflect, accurately we think, the spirit of the conferees, but it is not a faithful record of the papers presented at the conference.

Basic Homological Algebra

Author : M. Scott Osborne
Publisher : Springer Science & Business Media
ISBN 13 : 1461212782
Total Pages : 398 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Basic Homological Algebra by : M. Scott Osborne

Download or read book Basic Homological Algebra written by M. Scott Osborne and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especially appreciated the lively style of the book; [...] one is quickly able to find necessary details." EMS Newsletter

Homology Theory

Author : James W. Vick
Publisher : Springer Science & Business Media
ISBN 13 : 1461208815
Total Pages : 258 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Homology Theory by : James W. Vick

Download or read book Homology Theory written by James W. Vick and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.

Singular Homology Theory

Author : W.S. Massey
Publisher : Springer Science & Business Media
ISBN 13 : 1468492314
Total Pages : 278 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Singular Homology Theory by : W.S. Massey

Download or read book Singular Homology Theory written by W.S. Massey and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on homology and cohomology theory is geared towards the beginning graduate student. Singular homology theory is developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind various algebraic concepts is emphasized. The only formal prerequisites are knowledge of the basic facts of abelian groups and point set topology. Singular Homology Theory is a continuation of t he author's earlier book, Algebraic Topology: An Introduction, which presents such important supplementary material as the theory of the fundamental group and a thorough discussion of 2-dimensional manifolds. However, this earlier book is not a prerequisite for understanding Singular Homology Theory.

Modern General Topology

Author : J.-I. Nagata
Publisher : Elsevier
ISBN 13 : 0080933793
Total Pages : 533 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Modern General Topology by : J.-I. Nagata

Download or read book Modern General Topology written by J.-I. Nagata and published by Elsevier. This book was released on 1985-11-01 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work has been fundamentally revised to take account of recent developments in general topology. The first three chapters remain unchanged except for numerous minor corrections and additional exercises, but chapters IV-VII and the new chapter VIII cover the rapid changes that have occurred since 1968 when the first edition appeared. The reader will find many new topics in chapters IV-VIII, e.g. theory of Wallmann-Shanin's compactification, realcompact space, various generalizations of paracompactness, generalized metric spaces, Dugundji type extension theory, linearly ordered topological space, theory of cardinal functions, dyadic space, etc., that were, in the author's opinion, mostly special or isolated topics some twenty years ago but now settle down into the mainstream of general topology.

General Topology III

Author : A. V. Arhangel' skii
Publisher : Springer Science & Business Media
ISBN 13 : 3662074133
Total Pages : 238 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis General Topology III by : A. V. Arhangel' skii

Download or read book General Topology III written by A. V. Arhangel' skii and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference work deals with important topics in general topology and their role in functional analysis and axiomatic set theory, for graduate students and researchers working in topology, functional analysis, set theory and probability theory. It provides a guide to recent research findings, with three contributions by Arhangel'skii and Choban.

Elements of Homotopy Theory

Author : George W. Whitehead
Publisher : Springer Science & Business Media
ISBN 13 : 1461263182
Total Pages : 764 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Elements of Homotopy Theory by : George W. Whitehead

Download or read book Elements of Homotopy Theory written by George W. Whitehead and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems. Some acquaintance with manifolds and Poincare duality is desirable, but not essential. Anyone who has taught a course in algebraic topology is familiar with the fact that a formidable amount of technical machinery must be introduced and mastered before the simplest applications can be made. This phenomenon is also observable in the more advanced parts of the subject. I have attempted to short-circuit it by making maximal use of elementary methods. This approach entails a leisurely exposition in which brevity and perhaps elegance are sacrificed in favor of concreteness and ease of application. It is my hope that this approach will make homotopy theory accessible to workers in a wide range of other subjects-subjects in which its impact is beginning to be felt. It is a consequence of this approach that the order of development is to a certain extent historical. Indeed, if the order in which the results presented here does not strictly correspond to that in which they were discovered, it nevertheless does correspond to an order in which they might have been discovered had those of us who were working in the area been a little more perspicacious.

Elements of Functional Analysis

Author : Francis Hirsch
Publisher : Springer Science & Business Media
ISBN 13 : 1461214440
Total Pages : 399 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Elements of Functional Analysis by : Francis Hirsch

Download or read book Elements of Functional Analysis written by Francis Hirsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamental function spaces and their duals, explores operator theory and finally develops the theory of distributions up to significant applications such as Sobolev spaces and Dirichlet problems. Includes an assortment of well formulated exercises, with answers and hints collected at the end of the book.

Basic Notions of Algebra

Author : Igor R. Shafarevich
Publisher : Springer Science & Business Media
ISBN 13 : 9783540251774
Total Pages : 272 pages
Book Rating : 4.2/5 (517 download)

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Book Synopsis Basic Notions of Algebra by : Igor R. Shafarevich

Download or read book Basic Notions of Algebra written by Igor R. Shafarevich and published by Springer Science & Business Media. This book was released on 2005-04-13 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wholeheartedly recommended to every student and user of mathematics, this is an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields studied in every university maths course, through Lie groups to cohomology and category theory, the author shows how the origins of each concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Required reading for mathematicians, from beginners to experts.

Algebraic Topology - Homotopy and Homology

Author : Robert M. Switzer
Publisher : Springer
ISBN 13 : 3642619231
Total Pages : 541 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Algebraic Topology - Homotopy and Homology by : Robert M. Switzer

Download or read book Algebraic Topology - Homotopy and Homology written by Robert M. Switzer and published by Springer. This book was released on 2017-12-01 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The author has attempted an ambitious and most commendable project. [...] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature." Mathematical Reviews

Persistence Theory: From Quiver Representations to Data Analysis

Author : Steve Y. Oudot
Publisher : American Mathematical Soc.
ISBN 13 : 1470434431
Total Pages : 229 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Persistence Theory: From Quiver Representations to Data Analysis by : Steve Y. Oudot

Download or read book Persistence Theory: From Quiver Representations to Data Analysis written by Steve Y. Oudot and published by American Mathematical Soc.. This book was released on 2017-05-17 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

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.

Homology and Feynman Integrals

Author : Rudolph C. Hwa
Publisher :
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Homology and Feynman Integrals by : Rudolph C. Hwa

Download or read book Homology and Feynman Integrals written by Rudolph C. Hwa and published by . This book was released on 1966 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Homology

Author : Saunders MacLane
Publisher : Springer Science & Business Media
ISBN 13 : 3642620299
Total Pages : 436 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Homology by : Saunders MacLane

Download or read book Homology written by Saunders MacLane and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m~ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.

Advanced Linear Algebra

Author : Steven Roman
Publisher : Springer Science & Business Media
ISBN 13 : 0387728317
Total Pages : 528 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Advanced Linear Algebra by : Steven Roman

Download or read book Advanced Linear Algebra written by Steven Roman and published by Springer Science & Business Media. This book was released on 2007-09-20 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.

Rings of Continuous Functions

Author : Leonard Gillman
Publisher : Courier Dover Publications
ISBN 13 : 0486816885
Total Pages : 321 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Rings of Continuous Functions by : Leonard Gillman

Download or read book Rings of Continuous Functions written by Leonard Gillman and published by Courier Dover Publications. This book was released on 2018-01-16 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as a text as well as a treatise, the first systematic account of the theory of rings of continuous functions remains the basic graduate-level book in this area. 1960 edition.

Topological Methods in Data Analysis and Visualization III

Author : Peer-Timo Bremer
Publisher : Springer Science & Business
ISBN 13 : 3319040995
Total Pages : 276 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Topological Methods in Data Analysis and Visualization III by : Peer-Timo Bremer

Download or read book Topological Methods in Data Analysis and Visualization III written by Peer-Timo Bremer and published by Springer Science & Business. This book was released on 2014-04-22 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of peer-reviewed conference papers provides comprehensive coverage of cutting-edge research in topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The volume also features material on core research challenges such as the representation of large and complex datasets and integrating numerical methods with robust combinatorial algorithms. Reflecting the focus of the TopoInVis 2013 conference, the contributions evince the progress currently being made on finding experimental solutions to open problems in the sector. They provide an inclusive snapshot of state-of-the-art research that enables researchers to keep abreast of the latest developments and provides a foundation for future progress. With papers by some of the world’s leading experts in topological techniques, this volume is a major contribution to the literature in a field of growing importance with applications in disciplines that range from engineering to medicine.