Introduction to Metric and Topological Spaces

Author: Wilson A Sutherland
Publisher: Oxford University Press
ISBN: 9780199563074
Release Date: 2009-06-18
Genre: Mathematics

This fully updated new edition of Wilson Sutherland's classic text, Introduction to Metric and Topological Spaces, establishes the language of metric and topological spaces with continuity as the motivating concept, before developing its discussion to cover compactness, connectedness, and completeness.

Introduction to Metric and Topological Spaces

Author: Wilson Alexander Sutherland
Publisher: Oxford University Press
ISBN: 0198531613
Release Date: 1975
Genre: Science

One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This book introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces. The book is aimed primarily at the second-year mathematics student, and numerous exercises are included.

The Universal Coefficient Theorem and Quantum Field Theory

Author: Andrei-Tudor Patrascu
Publisher: Springer
ISBN: 9783319461434
Release Date: 2016-09-23
Genre: Science

This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.

Rough Set and Knowledge Technology

Author: JingTao Yao
Publisher: Springer Science & Business Media
ISBN: 9783642244247
Release Date: 2011-09-21
Genre: Computers

This book constitutes the refereed proceedings of the 6th International Conference on Rough Sets and Knowledge Technology, RSKT 2011, held in Banff, Canada, in September 2011. The 89 revised full papers presented together with 3 keynote lectures and 1 invited tutorial session were carefully reviewed and selected from 229 submissions. The papers are organized in topical sections on attribute reduction and feature selection, generalized rough set models, machine learning with rough and hybrid techniques, knowledge technology and intelligent systems and applications.

Approach Spaces

Author: Robert Lowen
Publisher: Oxford University Press
ISBN: 9780198500308
Release Date: 1997
Genre: Mathematics

In topology the three basic concepts of metrics, topologies and uniformities have been treated so far as separate entities by means of different methods and terminology. This is the first book to treat all three concepts as a special case of the concept of approach spaces. The book explains the richness of approach structures in great detail; it provides a comprehensive explanation of the categorical set-up, develops the basic theory and provides many examples,displaying links with various areas of mathematics such as approximation theory, probability theory, analysis and hyperspace theory.

Introduction to Uniform Spaces

Author: I. M. James
Publisher: Cambridge University Press
ISBN: 0521386209
Release Date: 1990-05-03
Genre: Mathematics

This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, much of which is published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces. Readers interested in general topology will find much to interest them here.

Featured Reviews in Mathematical Reviews 1997 1999

Author: Donald G. Babbitt
Publisher: American Mathematical Soc.
ISBN: 0821896709
Release Date: 2000-05-05
Genre: Mathematics

This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Distributionen Und Hilbertraumoperatoren

Author: Philippe Blanchard
Publisher: Springer
ISBN: 321182507X
Release Date: 1993-09-21
Genre: Science

Das Buch bietet eine Einführung in die zum Studium der Theoretischen Physik notwendigen mathematischen Grundlagen. Der erste Teil des Buches beschäftigt sich mit der Theorie der Distributionen und vermittelt daneben einige Grundbegriffe der linearen Funktionalanalysis. Der zweite Teil baut darauf auf und gibt eine auf das Wesentliche beschränkte Einführung in die Theorie der linearen Operatoren in Hilbert-Räumen. Beide Teile werden von je einer Übersicht begleitet, die die zentralen Ideen und Begriffe knapp erläutert und den Inhalt kurz beschreibt. In den Anhängen werden einige grundlegende Konstruktionen und Konzepte der Funktionalanalysis dargestellt und wichtige Konsequenzen entwickelt.

Einf hrung in die Funktionalanalysis

Author: Reinhold Meise
Publisher: Springer-Verlag
ISBN: 9783322803108
Release Date: 2013-03-07
Genre: Mathematics

Dieses Buch wendet sich an Studenten der Mathematik und der Physik, welche über Grundkenntnisse in Analysis und linearer Algebra verfügen.

Partielle Differentialgleichungen der Geometrie und der Physik 2

Author: Friedrich Sauvigny
Publisher: Springer-Verlag
ISBN: 9783540275404
Release Date: 2005-12-05
Genre: Mathematics

Das zweibändige Lehrbuch behandelt das Gebiet der partiellen Differentialgleichungen umfassend und anschaulich. Der Autor stellt in Band 2 funktionalanalytische Lösungsmethoden vor und erläutert u. a. die Lösbarkeit von Operatorgleichungen im Banachraum, lineare Operatoren im Hilbertraum und Spektraltheorie, die Schaudersche Theorie linearer elliptischer Differentialgleichungen sowie schwache Lösungen elliptischer Differentialgleichungen.

Undergraduate Topology

Author: Aisling McCluskey
Publisher: Oxford University Press
ISBN: 9780198702337
Release Date: 2014
Genre: Mathematics

This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors' combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp ideas precisely and to argue with straight and careful logic. Research and long experience in undergraduate mathematics education suggests that an optimal way to learn such a subject is to teach it to yourself, pro-actively, by guided reading of brief skeleton notes and by doing your own spadework to fill in the details and to flesh out the examples. This text will facilitate such an approach for those learners who opt to do it this way and for those instructors who would like to encourage this so-called 'Moore approach', even for a modest segment of the teaching term or for part of the class. In reality, most students simply do not have the combination of time, background and motivation needed to implement such a plan fully. The accessibility, flexibility and completeness of this text enable it to be used equally effectively for more conventional instructor-led courses. Critically, it furnishes a rich variety of exercises and examples, many of which have specimen solutions, through which to gain in confidence and competence.

Bulletin

Author:
Publisher:
ISBN: UOM:39015046023589
Release Date: 1977
Genre: Mathematics


ABPR

Author:
Publisher:
ISBN: STANFORD:36105210122334
Release Date: 1976
Genre: American literature


Introduction to Banach Spaces and Algebras

Author: Graham R. Allan
Publisher: Oxford University Press
ISBN: 9780199206537
Release Date: 2011
Genre: Banach algebras

A graduate level text in functional analysis, with an emphasis on Banach algebras. Based on lectures given for Part III of the Cambridge Mathematical Tripos, the text will assume a familiarity with elementary real and complex analysis, and some acquaintance with metric spaces, analytic topology and normed spaces (but not theorems depending on Baire category, or any version of the Hahn-Banach theorem).