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 ...
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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.
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Add this copy of Rings of Continuous Functions: 43 (the University to cart. $52.81, good condition, Sold by Fireside Bookshop rated 4.0 out of 5 stars, ships from Stroud, GLOUCESTERSHIRE, UNITED KINGDOM, published 1976 by Springer.
Add this copy of Rings of Continuous Functions to cart. $53.66, good condition, Sold by Fireside Bookshop rated 4.0 out of 5 stars, ships from Stroud, GLOUCESTERSHIRE, UNITED KINGDOM, published 1976 by Springer.
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Seller's Description:
Good in No d/j as Published jacket. Size: 8vo-over 7¾"-9¾" tall; Type: Book N.B. Small plain label to ffep. Light rubbing to head and tail of spine and corners of boards. Boards a little marked. Some light stains to ffep and front paste down.
Add this copy of Rings of Continous Functions-Undergraduate Texts to cart. $54.36, very good condition, Sold by Literary Cat Books rated 1.0 out of 5 stars, ships from Machynlleth, Powys, WALES, UNITED KINGDOM, published 1976 by Springer-Verlag.
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Seller's Description:
Very Good+ with no dust jacket. 0387901981. Slight wear to top and bottom of spine. Previous owners name written in blue pen on front pastedown.; Contains notes from previous owner. This classic text explores how the algebra of continuous real-valued functions reflects the topology of the space they're defined on. Blending point-set topology with commutative algebra, the book offers a deep and elegant introduction to topological algebra. Ideal for advanced undergraduates or early graduate students, it remains a foundational reference for those interested in the structure of function spaces and their connections to modern analysis.; 16.2x24.6x2.1cm; xiii, 300, (2) pages.
