The Theory of Sets of Points - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Theory of Sets of Points write by W. H. Young. This book was released on 2013-09-30. The Theory of Sets of Points available in PDF, EPUB and Kindle. 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."
Set Theory
Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Set Theory write by Abhijit Dasgupta. This book was released on 2013-12-11. Set Theory available in PDF, EPUB and Kindle. 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.
Point Set Theory
Point Set Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Point Set Theory write by Morgan. This book was released on 2018-04-27. Point Set Theory available in PDF, EPUB and Kindle. 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
THEORY OF SETS OF POINTS - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook THEORY OF SETS OF POINTS write by W. H. YOUNG. This book was released on 2018. THEORY OF SETS OF POINTS available in PDF, EPUB and Kindle.
Fixed Point Theory in Ordered Sets and Applications
Fixed Point Theory in Ordered Sets and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed Point Theory in Ordered Sets and Applications write by Siegfried Carl. This book was released on 2010-11-17. Fixed Point Theory in Ordered Sets and Applications available in PDF, EPUB and Kindle. This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained. Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.
