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 Topology
Point Set Topology - 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 Topology write by Steven A. Gaal. This book was released on 2009-04-23. Point Set Topology available in PDF, EPUB and Kindle. 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.
Elements of Point Set Topology
Elements of Point Set Topology - 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 Elements of Point Set Topology write by John D. Baum. This book was released on 1991-01-01. Elements of Point Set Topology available in PDF, EPUB and Kindle. 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.
Foundations of Point Set Theory
Foundations of 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 Foundations of Point Set Theory write by Robert Lee Moore. This book was released on 1932-12-31. Foundations of Point Set Theory available in PDF, EPUB and Kindle.
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.
