Rings of Continuous Functions

Rings of Continuous Functions
Author: Leonard Gillman
Publisher: Courier Dover Publications
Total Pages: 321
Release: 2018-01-16
Genre: Mathematics
ISBN: 0486816885

Designed as a text as well as a treatise, the first systematic account of the theory of rings of continuous functions remains the basic graduate-level book in this area. 1960 edition.

Rings of Continuous Functions

Rings of Continuous Functions
Author: Leonard Gillman
Publisher: Courier Dover Publications
Total Pages: 321
Release: 2017-11-29
Genre: Mathematics
ISBN: 0486827453

Designed as a text as well as a treatise, the first systematic account of the theory of rings of continuous functions remains the basic graduate-level book in this area. 1960 edition.

Rings of Continuous Functions

Rings of Continuous Functions
Author: L. Gillman
Publisher: Springer Science & Business Media
Total Pages: 307
Release: 2013-06-29
Genre: Medical
ISBN: 1461578191

This book is addressed to those who know the meaning of each word in the title: none is defined in the text. The reader can estimate the knowledge required by looking at Chapter 0; he should not be dis couraged, however, if he finds some of its material unfamiliar or the presentation rather hurried. Our objective is a systematic study of the ring C(X) of all real-valued continuous functions on an arbitrary topological space X. We are con cerned with algebraic properties of C(X) and its subring C*(X) of bounded functions and with the interplay between these properties and the topology of the space X on which the functions are defined. Major emphasis is placed on the study of ideals, especially maximal ideals, and on their associated residue class rings. Problems of extending continuous functions from a subspace to the entire space arise as a necessary adjunct to this study and are dealt with in considerable detail. The contents of the book fall naturally into three parts. The first, comprising Chapters 1 through 5 and the beginning of Chapter 10, presents the fundamental aspects of the subject insofar as they can be discussed without introducing the Stone-Cech compactification. In Chapter 3, the study is reduced to the case of completely regular spaces.

Spaces of Continuous Functions

Spaces of Continuous Functions
Author: G.L.M. Groenewegen
Publisher: Springer
Total Pages: 183
Release: 2016-06-17
Genre: Mathematics
ISBN: 9462392013

The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given.Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem.The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.

General Topology

General Topology
Author: Stephen Willard
Publisher: Courier Corporation
Total Pages: 386
Release: 2012-07-12
Genre: Mathematics
ISBN: 0486131785

Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.

Topological Rings

Topological Rings
Author: S. Warner
Publisher: Elsevier
Total Pages: 509
Release: 1993-07-07
Genre: Mathematics
ISBN: 0080872891

This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included.The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn's Lemma, is also expected.

Rings of Continuous Function

Rings of Continuous Function
Author: Aull
Publisher: CRC Press
Total Pages: 337
Release: 2020-12-17
Genre: Mathematics
ISBN: 1000111113

This book contains papers on algebra, functional analysis, and general topology, with a strong interaction with set theoretic axioms and involvement with category theory, presented in the special session on Rings of Continuous Functions held in 1982 in Cincinnati, Ohio.

Exercises in Basic Ring Theory

Exercises in Basic Ring Theory
Author: Grigore Calugareanu
Publisher: Springer Science & Business Media
Total Pages: 226
Release: 1998-02-28
Genre: Mathematics
ISBN: 9780792349181

Each undergraduate course of algebra begins with basic notions and results concerning groups, rings, modules and linear algebra. That is, it begins with simple notions and simple results. Our intention was to provide a collection of exercises which cover only the easy part of ring theory, what we have named the "Basics of Ring Theory". This seems to be the part each student or beginner in ring theory (or even algebra) should know - but surely trying to solve as many of these exercises as possible independently. As difficult (or impossible) as this may seem, we have made every effort to avoid modules, lattices and field extensions in this collection and to remain in the ring area as much as possible. A brief look at the bibliography obviously shows that we don't claim much originality (one could name this the folklore of ring theory) for the statements of the exercises we have chosen (but this was a difficult task: indeed, the 28 titles contain approximatively 15.000 problems and our collection contains only 346). The real value of our book is the part which contains all the solutions of these exercises. We have tried to draw up these solutions as detailed as possible, so that each beginner can progress without skilled help. The book is divided in two parts each consisting of seventeen chapters, the first part containing the exercises and the second part the solutions.

Basic Category Theory

Basic Category Theory
Author: Tom Leinster
Publisher: Cambridge University Press
Total Pages: 193
Release: 2014-07-24
Genre: Mathematics
ISBN: 1107044243

A short introduction ideal for students learning category theory for the first time.