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The Theory of Sets of Points

2013-09-30 Mathematics
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Release : 2013-09-30
Genre : Mathematics
Kind : eBook
Book Rating : 623/5 ( reviews)

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Book Synopsis The Theory of Sets of Points by : W. H. Young

Download or read book The Theory of Sets of Points written by W. H. Young. This book was released on 2013-09-30. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Point Set Theory

2018-04-27 Mathematics
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Release : 2018-04-27
Genre : Mathematics
Kind : eBook
Book Rating : 797/5 ( reviews)

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Book Synopsis Point Set Theory by : Morgan

Download or read book Point Set Theory written by Morgan. This book was released on 2018-04-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.

THEORY OF SETS OF POINTS

2018
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Release : 2018
Genre :
Kind : eBook
Book Rating : 258/5 ( reviews)

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Book Synopsis THEORY OF SETS OF POINTS by : W. H. YOUNG

Download or read book THEORY OF SETS OF POINTS written by W. H. YOUNG. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt:

Set Theory

2013-12-11 Mathematics
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Release : 2013-12-11
Genre : Mathematics
Kind : eBook
Book Rating : 540/5 ( reviews)

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Book Synopsis Set Theory by : Abhijit Dasgupta

Download or read book Set Theory written by Abhijit Dasgupta. This book was released on 2013-12-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Theory of Sets of Points (Classic Reprint)

2017-11-20 Mathematics
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Release : 2017-11-20
Genre : Mathematics
Kind : eBook
Book Rating : 162/5 ( reviews)

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Book Synopsis The Theory of Sets of Points (Classic Reprint) by : W. H. Young

Download or read book The Theory of Sets of Points (Classic Reprint) written by W. H. Young. This book was released on 2017-11-20. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Theory of Sets of Points The difficulties in arrangement which this fact, suggests have been enhanced by the nature of the subject itself and by the tentative character of some of its results. The writing of the book has necessarily involved attempts to extend the frontier of existing knowledge, and to fill in gaps which broke the connexion between isolated parts of the subject. The' references in the text which do not give the name of the author always refer to my own papers; in this connexion, however, I should like to out that the citations in the text are not to be regarded any means complete, and are supplemented by the list of literature at the end of the volume. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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