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International Journal of Mathematics and Mathematical Sciences
Volume 18, Issue 4, Pages 701-704
http://dx.doi.org/10.1155/S0161171295000895

Gelfand theorem implies Stone representation theorem of Boolean rings

Department of Mathematics, The Catholic University of America, Washington 20064, DC, USA

Received 27 June 1994; Revised 9 September 1994

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Stone Theorem about representing a Boolean algebra in terms of open-closed subsets of a topological space is a consequence of the Gelfand Theorem about representing a B- algebra as the algebra of continuous functions on a compact Hausdorff space.