Rings of Continuous Functions
Published in October 1976
Book
Hardback
XIII, 300 pages
978-3-540-90198-3 (ISBN)
Description
The objective of this book is the systematic study of the ring of all real valued continuous functions on arbitrary topological spaces. Great emphasis is placed on the study of ideals, and on the associated residue class rings. Questions of extending continuous functions from a subspace to the entire space arise as a necessary adjunct and are dealt with in considerable detail. Many problems provide additional information about the material covered in the text.
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Content
Contents: Functions of a Topological Space.- Ideals and Z-Filters.- Completely Regular Spaces.- Fixed Ideals. Compact Spaces.- Ordered Residue Class Rings.- The Stone-Czech Compactification.- Characterization of Maximal Ideals.- Realcompact Spaces.- Cardinals of Closed Sets in Beta-x.- Homomorphisms and Continuous Mappings.- Embedding in Products of Real Lines.- Discrete Spaces. Nonmeasurable Cardinals.- Hyper-Real Residue Class Fields.- Prime Ideals.- Uni- form Spaces.- Dimension.- Notes.- Bibliography.- List of Symbols.- Index.