International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 1, Pages 87-92
doi:10.1155/S0161171278000113
A note on rings of continous functions
Department of Mathematics and Computer Science, University of South Carolina, Columbia 29208, South Carolina, USA
Received 9 January 1978; Revised 7 March 1978
Copyright © 1978 J. S. Yang. 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
For a topological space X, and a topological ring A, let C(X,A) be the ring of all continuous functions from X into A under the pointwise multiplication. We show that the theorem “there is a completely regular space Y associated with a given topological space X such that C(Y,R) is isomorphic to C(X,R)” may be extended to a fairly large class of topologlcal
rings, and that, in the study of algebraic structure of the ring C(X,A), it is sufficient to study C(X,R) if A is path connected.