Read Rings of Continuous Functions (The university series in higher mathematics)

Rings of Continuous Functions (The university series in higher mathematics)

Leonard Gillman

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Description: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."We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Rings of Continuous Functions (The university series in higher mathematics). To get started finding Rings of Continuous Functions (The university series in higher mathematics), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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ISBN: 0387901981

Description: 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."We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Rings of Continuous Functions (The university series in higher mathematics). To get started finding Rings of Continuous Functions (The university series in higher mathematics), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Rings of Continuous Functions (The university series in higher mathematics)

Rings of Continuous Functions (The university series in higher mathematics)

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