From Sets And Types To Topology And Analysis

Author : Laura Crosilla,Peter Schuster
Publisher : Clarendon Press
Page : 372 pages
File Size : 42,8 Mb
Release : 2005-10-06
Category : Mathematics
ISBN : 9780191524202

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From Sets and Types to Topology and Analysis by Laura Crosilla,Peter Schuster Pdf

This edited collection bridges the foundations and practice of constructive mathematics and focusses on the contrast between the theoretical developments, which have been most useful for computer science (eg constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logicians, mathematicians, philosophers and computer scientists Including, with contributions from leading researchers, it is up-to-date, highly topical and broad in scope. This is the latest volume in the Oxford Logic Guides, which also includes: 41. J.M. Dunn and G. Hardegree: Algebraic Methods in Philosophical Logic 42. H. Rott: Change, Choice and Inference: A study of belief revision and nonmonotoic reasoning 43. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 1 44. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 2 45. David J. Pym and Eike Ritter: Reductive Logic and Proof Search: Proof theory, semantics and control 46. D.M. Gabbay and L. Maksimova: Interpolation and Definability: Modal and Intuitionistic Logics 47. John L. Bell: Set Theory: Boolean-valued models and independence proofs, third edition

Author : Laura Crosilla,Peter Schuster
Publisher : Oxford University Press on Demand
Page : 371 pages
File Size : 49,7 Mb
Release : 2005-10-06
Category : Mathematics
ISBN : 9780198566519

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From Sets and Types to Topology and Analysis by Laura Crosilla,Peter Schuster Pdf

Bridging the foundations and practice of constructive mathematics, this text focusses on the contrast between the theoretical developments - which have been most useful for computer science - and more specific efforts on constructive analysis, algebra and topology.

Author : John D. Baum
Publisher : Courier Corporation
Page : 164 pages
File Size : 52,7 Mb
Release : 1991-01-01
Category : Mathematics
ISBN : 9780486668260

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Elements of Point Set Topology by John D. Baum Pdf

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.

Author : Douglas Bridges,Hajime Ishihara,Michael Rathjen,Helmut Schwichtenberg
Publisher : Cambridge University Press
Page : 864 pages
File Size : 44,6 Mb
Release : 2023-03-31
Category : Mathematics
ISBN : 9781009041416

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Handbook of Constructive Mathematics by Douglas Bridges,Hajime Ishihara,Michael Rathjen,Helmut Schwichtenberg Pdf

Constructive mathematics – mathematics in which 'there exists' always means 'we can construct' – is enjoying a renaissance. fifty years on from Bishop's groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of mathematics and to have profound influence in theoretical computer science. This handbook gives the most complete overview of modern constructive mathematics, with contributions from leading specialists surveying the subject's myriad aspects. Major themes include: constructive algebra and geometry, constructive analysis, constructive topology, constructive logic and foundations of mathematics, and computational aspects of constructive mathematics. A series of introductory chapters provides graduate students and other newcomers to the subject with foundations for the surveys that follow. Edited by four of the most eminent experts in the field, this is an indispensable reference for constructive mathematicians and a fascinating vista of modern constructivism for the increasing number of researchers interested in constructive approaches.

Author : Erich Grädel,Reinhard Kahle
Publisher : Springer Science & Business Media
Page : 577 pages
File Size : 49,7 Mb
Release : 2009-08-28
Category : Computers
ISBN : 9783642040269

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Computer Science Logic by Erich Grädel,Reinhard Kahle Pdf

This book constitutes the proceedings of the 23rd International Workshop on Computer Science Logic, CSL 2009, held in Coimbra, Portugal, in September 2009. The 34 papers presented together with 5 invited talks were carefully reviewed and selected from 89 full paper submissions. All current aspects of logic in computer science are addressed, ranging from foundational and methodological issues to application issues of practical relevance. The book concludes with a presentation of this year's Ackermann award, the EACSL Outstanding Dissertation Award for Logic in Computer Science.

Author : Albert Wilansky
Publisher : Courier Corporation
Page : 399 pages
File Size : 54,8 Mb
Release : 2008-10-17
Category : Mathematics
ISBN : 9780486469034

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Topology for Analysis by Albert Wilansky Pdf

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.

Author : Steven G. Krantz
Publisher : CRC Press
Page : 422 pages
File Size : 48,7 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 : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 44,8 Mb
Release : 2022-03-10
Category : Computers
ISBN : 9781009098168

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Computational Topology for Data Analysis by Tamal Krishna Dey,Yusu Wang Pdf

This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.

Author : Anonim
Publisher : Unknown
Page : 984 pages
File Size : 50,9 Mb
Release : 2006
Category : Mathematics
ISBN : UOM:39015067268261

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Mathematical Reviews by Anonim Pdf

Author : T. Husain
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461587989

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Topology and Maps by T. Husain Pdf

This work is suitable for undergraduate students as well as advanced students and research workers. It consists of ten chapters, the first six of which are meant for beginners and are therefore suitable for undergraduate students; Chapters VII-X are suitable for advanced students and research workers interested in functional analysis. This book has two special features: First, it contains generalizations of continuous maps on topological spaces, e. g. , almost continuous maps, nearly continuous maps, maps with closed graph, graphically continuous maps, w-continuous maps, and a-continuous maps, etc. and some of their properties. The treatment of these notions appears here, in Chapter VII, for the first time in book form. The second feature consists in some not-so-easily-available nuptial delights that grew out of the marriage of topology and functional analysis; they are topics mainly courted by functional analysts and seldom given in topology books. Specifically, one knows that the set C(X) of all real- or com plex-valued continuous functions on a completely regular space X forms a locally convex topological algebra, a fortiori a topological vector space, in the compact-open topology. A number of theorems are known: For example, C(X) is a Banach space iff X is compact, or C(X) is complete iff X is a kr-space, and so on. Chapters VIII and X include this material, which, to the regret of many interested readers has not previously been available in book form (a recent publication (Weir [\06]) does, however, contain some material of our Chapter X).

Author : Isabelle Comyn-Wattiau,Katsumi Tanaka,Il-Yeol Song,Shuichiro Yamamoto,Motoshi Saeki
Publisher : Springer
Page : 562 pages
File Size : 48,7 Mb
Release : 2016-11-07
Category : Computers
ISBN : 9783319463971

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Conceptual Modeling by Isabelle Comyn-Wattiau,Katsumi Tanaka,Il-Yeol Song,Shuichiro Yamamoto,Motoshi Saeki Pdf

This book constitutes the refereed proceedings of the 345h International Conference on Conceptual Modeling, ER 2016, held in Gifu, Japan, in November 2016. The 23 full and 18 short papers presented together with 3 keynotes were carefully reviewed and selected from 113 submissions. The papers are organized in topical sections on Analytics and Conceptual Modeling; Conceptual Modeling and Ontologies; Requirements Engineering; Advanced Conceptual Modeling; Semantic Annotations; Modeling and Executing Business Processes; Business Process Management and Modeling; Applications and Experiments of Conceptual Modeling; Schema Mapping; Conceptual Modeling Guidance; and Goal Modeling.

Author : Kazimierz Kuratowski
Publisher : Elsevier
Page : 352 pages
File Size : 54,7 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483151632

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Introduction to Set Theory and Topology by Kazimierz Kuratowski Pdf

Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

Author : Eric Yu,Gillian Dobbie,Matthias Jarke,Sandeep Purao
Publisher : Springer
Page : 476 pages
File Size : 46,5 Mb
Release : 2014-10-10
Category : Computers
ISBN : 9783319122069

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Conceptual Modeling by Eric Yu,Gillian Dobbie,Matthias Jarke,Sandeep Purao Pdf

This book constitutes the refereed proceedings of the 32nd International Conference on Conceptual Modeling, ER 2014, held in Atlanta, GA, USA. The 23 full and 15 short papers presented were carefully reviewed and selected from 80 submissions. Topics of interest presented and discussed in the conference span the entire spectrum of conceptual modeling including research and practice in areas such as: data on the web, unstructured data, uncertain and incomplete data, big data, graphs and networks, privacy and safety, database design, new modeling languages and applications, software concepts and strategies, patterns and narratives, data management for enterprise architecture, city and urban applications.

Author : Ting-Li Yang,Anxin Liu,Huiping Shen,LuBin Hang,Yufeng Luo,Qiong Jin
Publisher : Springer
Page : 236 pages
File Size : 40,5 Mb
Release : 2018-01-02
Category : Technology & Engineering
ISBN : 9789811055324

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Topology Design of Robot Mechanisms by Ting-Li Yang,Anxin Liu,Huiping Shen,LuBin Hang,Yufeng Luo,Qiong Jin Pdf

This book focuses on the topology theory of mechanisms developed by the authors and provides a systematic method for the topology design of robot mechanisms. The main original theoretical contributions of this book include: A. Three basic concepts · The “geometrical constraint type of axes” is introduced as the third element of the topological structure of a mechanism. When it is combined with the other two elements, the kinematic pair and the connection of links, the symbolic expression of the topological structure is independent of the motion positions (except for the singularity positions) and the fixed coordinate system (Chapter 2). · The position and orientation characteristic (POC) set is used to describe the POC of the relative motion between any two links. The POC set, derived from the unit vector set of the velocity of a link, is only depend on the topological structure of a mechanism. Therefore, it is also independent of the motion positions and the fixed coordinate system (Chapter 3). · The single open chain (SOC) unit is the base unit of the topological structure used to develop the four basic equations of the mechanism topology (Chapters 2, 4–6). B. The mechanism composition principle based on the SOC units This book proposes a mechanism composition principle, based on the SOC units, to establish a systematic theory for the unified modeling of the topology, kinematics, and dynamics of mechanisms based on the SOC units (Chapter 7). C. Four basic equations • The POC equation of serial mechanisms with 10 symbolic operation rules (Chapter 4). • The POC equation of parallel mechanisms with 14 symbolic operation rules (Chapter 5). • The general DOF formula for spatial mechanisms (Chapter 6). • The coupling degree formula for the Assur kinematic chain (Chapter 7). D. One systematic method for the topology design of robot mechanisms (Chapters 8–10) Based on the three basic concepts and the four basic equations addressed above, this book puts forward a systematic method for the topology design of parallel mechanisms, which is fundamentally different from all existing methods. Its main characteristics are as follows: • The design process includes two stages: the first is structure synthesis, which derives many structure types; the second involves the performance analysis, classification and optimization of structure types derived from the first stage. • The design operation is independent of the motion positions and the fixed coordinate system. Therefore, the proposed method is essentially a geometrical method, which ensures the full-cycle DOF and the generality of geometric conditions of mechanism existence. • Each individual design step follows an explicit formula or the guidelines for design criteria, making the operation simple, feasible and reproducible. In addition, the topology design of the SCARA PMs is studied in detail to demonstrate the proposed method (Chapter 10).

Author : Steven A. Gaal
Publisher : Unknown
Page : 340 pages
File Size : 54,9 Mb
Release : 1964
Category : Set theory
ISBN : STANFORD:36105033159299

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Point Set Topology by Steven A. Gaal Pdf

This book presents point set topology not only as an end in itself, but as a related discipline to the proper understanding of various branches of analysis and geometry. It starts with the basic concepts of set theory and topological spaces and ends with the beginning of functional analysis. The text and nearly all of the exercises presuppose knowledge of only those concepts defined within, so the book can serve as a self-contained course in topology for independent study.