Rings of Continuous Functions in the 1950s

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Book Chapter


Mathematics (HMC)

Publication Date



What follows is the author’s recollection of the early development of rings of continuous functions with emphasis on the work done in the 1950s at Purdue University. No pretense is made of thoroughness or historical scholarship. Some of the work done since that time is discussed, and references to books and survey articles are included. The terminology used below is, by and large, that of the great text by L. Gillman and M. Jerison [17]. In particular, for any topological space X, C(X) will denote the ring of all continuous functions f : X → ℝ under the usual pointwise operations, where ℝ denotes the real field with its usual order and topology, and C* (X) denotes its subring of bounded continuous functions.

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© 1997 Springer