A note on rings of continous functions
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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1978-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171278000113 |
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |