A note on rings of continous functions

• Main Author: J. S. Yang
• Format: Article
• Language: English
• Published: Hindawi Limited 1978-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Subjects: continuous functions; completely regular space; topological ring; S-pair; compact-open topology.
• Online Access: http://dx.doi.org/10.1155/S0161171278000113

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.