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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1978-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171278000113 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552588036276224 |
|---|---|
| author | J. S. Yang |
| author_facet | J. S. Yang |
| author_sort | J. S. Yang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b9da00fdd5cb44d495e2f39625763d2b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1978-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b9da00fdd5cb44d495e2f39625763d2b2025-02-03T05:58:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251978-01-0111879210.1155/S0161171278000113A note on rings of continous functionsJ. S. Yang0Department of Mathematics and Computer Science, University of South Carolina, Columbia 29208, South Carolina, USAFor 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.http://dx.doi.org/10.1155/S0161171278000113continuous functionscompletely regular spacetopological ringS-paircompact-open topology. |
| spellingShingle | J. S. Yang A note on rings of continous functions International Journal of Mathematics and Mathematical Sciences continuous functions completely regular space topological ring S-pair compact-open topology. |
| title | A note on rings of continous functions |
| title_full | A note on rings of continous functions |
| title_fullStr | A note on rings of continous functions |
| title_full_unstemmed | A note on rings of continous functions |
| title_short | A note on rings of continous functions |
| title_sort | note on rings of continous functions |
| topic | continuous functions completely regular space topological ring S-pair compact-open topology. |
| url | http://dx.doi.org/10.1155/S0161171278000113 |
| work_keys_str_mv | AT jsyang anoteonringsofcontinousfunctions AT jsyang noteonringsofcontinousfunctions |