Ring of continuous function in 1950s

Document Type : Translation Paper

Author

Shahid Chamran University

Abstract

This paper is a translation of the the following paper into Persian:
[Melvim Henriksen, Ring of Continuous Function in 1950s, Handbook of the History of General Topology, 1 (1997) 243-253.]
 

What follows is the authors 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 [L. Gillman and M. Jerison, Rings of continuous functions, D. Van Nostrand Publ. Co., New York, 1960]. In particular, for any topological space $X$, $C(X)$ will denote the ring of all continuous functions $f:X\to \Bbb{R}$ under the usual pointwise operations, where $\Bbb{R}$ denotes the real field with its usual order and topology, and $C^*(X)$ denotes its subring of bounded continuous functions.

Keywords

References

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History

  • Receive Date: 14 December 2013
  • Revise Date: 11 March 2014
  • Accept Date: 12 April 2014
  • Publish Date: 22 August 2016

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