International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1978 / Article

Open Access

Volume 1 |Article ID 535619 | https://doi.org/10.1155/S0161171278000113

J. S. Yang, "A note on rings of continous functions", International Journal of Mathematics and Mathematical Sciences, vol. 1, Article ID 535619, 6 pages, 1978. https://doi.org/10.1155/S0161171278000113

A note on rings of continous functions

Received09 Jan 1978
Revised07 Mar 1978

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.

Copyright © 1978 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.


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