Point Set Theory

Author : Morgan
Publisher : Routledge
Page : 208 pages
File Size : 40,7 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9781351423793

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Point Set Theory by Morgan Pdf

Investigations by Baire, Lebesgue, Hausdorff, Marczewski, and othes have culminated invarious schemes for classifying point sets. This important reference/text bringstogether in a single theoretical framework the properties common to these classifications.Providing a clear, thorough overview and analysis of the field, Point Set Theoryutilizes the axiomatically determined notion of a category base for extending generaltopological theorems to a higher level of abstraction ... axiomatically unifies analogiesbetween Baire category and Lebesgue measure . .. enhances understanding of thematerial with numerous examples and discussions of abstract concepts ... and more.Imparting a solid foundation for the modem theory of real functions and associated areas,this authoritative resource is a vital reference for set theorists, logicians, analysts, andresearch mathematicians involved in topology, measure theory, or real analysis. It is anideal text for graduate mathematics students in the above disciplines who havecompleted undergraduate courses in set theory and real analysis.

Author : Abhijit Dasgupta
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 48,9 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461488545

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Set Theory by Abhijit Dasgupta Pdf

What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.

Author : John D. Baum
Publisher : Courier Corporation
Page : 164 pages
File Size : 45,7 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 : Robert Lee Moore
Publisher : American Mathematical Soc.
Page : 419 pages
File Size : 43,5 Mb
Release : 1932-12-31
Category : Mathematics
ISBN : 9780821810132

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Foundations of Point Set Theory by Robert Lee Moore Pdf

Author : Steven A. Gaal
Publisher : Courier Corporation
Page : 338 pages
File Size : 43,7 Mb
Release : 2009-04-23
Category : Mathematics
ISBN : 9780486472225

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Point Set Topology by Steven A. Gaal Pdf

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.

Author : John B. Conway
Publisher : Springer Science & Business Media
Page : 142 pages
File Size : 54,7 Mb
Release : 2013-11-04
Category : Mathematics
ISBN : 9783319023687

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A Course in Point Set Topology by John B. Conway Pdf

This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.

Author : W. H. Young,Grace Chisholm Young
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 47,6 Mb
Release : 2013-09-30
Category : Electronic
ISBN : 9781470409623

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The Theory of Sets of Points by W. H. Young,Grace Chisholm Young Pdf

From the Preface to the first edition (1906): "A few of the most modern books on the Theory of Functions devote some pages to the establishment of certain results belonging to our subject, and required for the special purposes in hand... But we may fairly claim that the present work is the first attempt at a systematic exposition of the subject as a whole."

Author : Stephen Willard
Publisher : Courier Corporation
Page : 386 pages
File Size : 49,8 Mb
Release : 2012-07-12
Category : Mathematics
ISBN : 9780486131788

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General Topology by Stephen Willard Pdf

Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.

Author : R. Vaidyanathaswamy
Publisher : Courier Corporation
Page : 292 pages
File Size : 46,6 Mb
Release : 1960-01-01
Category : Mathematics
ISBN : 0486404560

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Set Topology by R. Vaidyanathaswamy Pdf

This introductory text covers the algebra of subsets and of rings and fields of sets, complementation and ideal theory in the distributive lattice, closure function, neighborhood topology, much more. Includes numerous exercises. 1960 edition.

Author : Andre L. Yandl,Adam Bowers
Publisher : Courier Dover Publications
Page : 256 pages
File Size : 42,5 Mb
Release : 2016-04-10
Category : Mathematics
ISBN : 9780486811017

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Elementary Point-Set Topology by Andre L. Yandl,Adam Bowers Pdf

In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations. "This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America

Author : K. Kunen,J. Vaughan
Publisher : Elsevier
Page : 1282 pages
File Size : 55,5 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483295152

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Handbook of Set-Theoretic Topology by K. Kunen,J. Vaughan Pdf

This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest. In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

Author : Herbert B. Enderton
Publisher : Academic Press
Page : 279 pages
File Size : 44,5 Mb
Release : 1977-05-23
Category : Mathematics
ISBN : 9780080570426

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Elements of Set Theory by Herbert B. Enderton Pdf

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

Author : Jean Goubault-Larrecq
Publisher : Cambridge University Press
Page : 499 pages
File Size : 45,7 Mb
Release : 2013-03-28
Category : Mathematics
ISBN : 9781107328778

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Non-Hausdorff Topology and Domain Theory by Jean Goubault-Larrecq Pdf

This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself. Graduate students and researchers alike will enjoy exploring this treasure trove of results. Full proofs are given, as well as motivating ideas, clear explanations, illuminating examples, application exercises and some more challenging problems for more advanced readers.

Author : Jose Ferreiros
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 49,6 Mb
Release : 2001-11-01
Category : Mathematics
ISBN : 3764357495

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Labyrinth of Thought by Jose Ferreiros Pdf

"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

Author : Morgan
Publisher : CRC Press
Page : 300 pages
File Size : 53,5 Mb
Release : 1989-10-23
Category : Mathematics
ISBN : 0824781783

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Point Set Theory by Morgan Pdf

This book provides a systematic treatment of properties common to the classifications of point sets. It unifies analogies between Baire category and Lebesgue measure by carrying general topological concepts to a higher level of abstraction. The book is intended for graduate mathematics students.