Set Theory And Metric Spaces PDF Download
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| Author | : Irving Kaplansky |
| Publisher | : American Mathematical Society |
| Total Pages | : 140 |
| Release | : 2020-09-10 |
| Genre | : Mathematics |
| ISBN | : 1470463849 |
Download Set Theory and Metric Spaces Book in PDF, ePub and Kindle
This is a book that could profitably be read by many graduate students or by seniors in strong major programs … has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. … There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem … The presentation of metric spaces before topological spaces … should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar. —Canadian Mathematical Bulletin Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent. — Lance Small, UC San Diego This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.
| Author | : Irving Kaplansky |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 154 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821826948 |
Download Set Theory and Metric Spaces Book in PDF, ePub and Kindle
This is a book that could profitably be read by many graduate students or by seniors in strong major programs ... has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. ... There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem ... The presentation of metric spaces before topological spaces ... should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar. --Canadian Mathematical Bulletin Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent. -- Lance Small, UC San Diego This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.
| Author | : Phil Diamond |
| Publisher | : World Scientific |
| Total Pages | : 192 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 9789810217310 |
Download Metric Spaces of Fuzzy Sets Book in PDF, ePub and Kindle
The primary aim of the book is to provide a systematic development of the theory of metric spaces of normal, upper semicontinuous fuzzy convex fuzzy sets with compact support sets, mainly on the base space ?n. An additional aim is to sketch selected applications in which these metric space results and methods are essential for a thorough mathematical analysis.This book is distinctly mathematical in its orientation and style, in contrast with many of the other books now available on fuzzy sets, which, although all making use of mathematical formalism to some extent, are essentially motivated by and oriented towards more immediate applications and related practical issues. The reader is assumed to have some previous undergraduate level acquaintance with metric spaces and elementary functional analysis.
| Author | : Mohamed A. Khamsi |
| Publisher | : John Wiley & Sons |
| Total Pages | : 318 |
| Release | : 2011-10-14 |
| Genre | : Mathematics |
| ISBN | : 1118031326 |
Download An Introduction to Metric Spaces and Fixed Point Theory Book in PDF, ePub and Kindle
Diese Einfuhrung in das Gebiet der metrischen Raume richtet sich in erster Linie nicht an Spezialisten, sondern an Anwender der Methode aus den verschiedensten Bereichen der Naturwissenschaften. Besonders ausfuhrlich und anschaulich werden die Grundlagen von metrischen Raumen und Banach-Raumen erklart, Anhange enthalten Informationen zu verschiedenen Schlusselkonzepten der Mengentheorie (Zornsches Lemma, Tychonov-Theorem, transfinite Induktion usw.). Die hinteren Kapitel des Buches beschaftigen sich mit fortgeschritteneren Themen.
| Author | : Mícheál O'Searcoid |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 318 |
| Release | : 2006-12-26 |
| Genre | : Mathematics |
| ISBN | : 1846286271 |
Download Metric Spaces Book in PDF, ePub and Kindle
The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.
| Author | : Robert B. Ash |
| Publisher | : Courier Corporation |
| Total Pages | : 216 |
| Release | : 2014-07-28 |
| Genre | : Mathematics |
| ISBN | : 0486151492 |
Download Real Variables with Basic Metric Space Topology Book in PDF, ePub and Kindle
Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis. The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.
| Author | : Alexander Kechris |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 419 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461241901 |
Download Classical Descriptive Set Theory Book in PDF, ePub and Kindle
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.
| Author | : K. R. Parthasarathy |
| Publisher | : Academic Press |
| Total Pages | : 289 |
| Release | : 2014-07-03 |
| Genre | : Mathematics |
| ISBN | : 1483225259 |
Download Probability Measures on Metric Spaces Book in PDF, ePub and Kindle
Probability Measures on Metric Spaces presents the general theory of probability measures in abstract metric spaces. This book deals with complete separable metric groups, locally impact abelian groups, Hilbert spaces, and the spaces of continuous functions. Organized into seven chapters, this book begins with an overview of isomorphism theorem, which states that two Borel subsets of complete separable metric spaces are isomorphic if and only if they have the same cardinality. This text then deals with properties such as tightness, regularity, and perfectness of measures defined on metric spaces. Other chapters consider the arithmetic of probability distributions in topological groups. This book discusses as well the proofs of the classical extension theorems and existence of conditional and regular conditional probabilities in standard Borel spaces. The final chapter deals with the compactness criteria for sets of probability measures and their applications to testing statistical hypotheses. This book is a valuable resource for statisticians.
| Author | : Satish Shirali |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 238 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9781852339227 |
Download Metric Spaces Book in PDF, ePub and Kindle
One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily
| Author | : Dhananjay Gopal |
| Publisher | : CRC Press |
| Total Pages | : 303 |
| Release | : 2020-07-14 |
| Genre | : Mathematics |
| ISBN | : 1000087999 |
Download An Introduction to Metric Spaces Book in PDF, ePub and Kindle
This book serves as a textbook for an introductory course in metric spaces for undergraduate or graduate students. The goal is to present the basics of metric spaces in a natural and intuitive way and encourage students to think geometrically while actively participating in the learning of this subject. In this book, the authors illustrated the strategy of the proofs of various theorems that motivate readers to complete them on their own. Bits of pertinent history are infused in the text, including brief biographies of some of the central players in the development of metric spaces. The textbook is divided into seven chapters that contain the main materials on metric spaces; namely, introductory concepts, completeness, compactness, connectedness, continuous functions and metric fixed point theorems with applications. Some of the noteworthy features of this book include · Diagrammatic illustrations that encourage readers to think geometrically · Focus on systematic strategy to generate ideas for the proofs of theorems · A wealth of remarks, observations along with a variety of exercises · Historical notes and brief biographies appearing throughout the text
