Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-15T17:34:57.630Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Certain Subalgebras of C()

Published online by Cambridge University Press:  20 November 2018

Anthony W. Hager  and
Donald G. Johnson
Anthony W. Hager
Affiliation:
The University oj Rochester, Rochester, New York
Donald G. Johnson
Affiliation:
The New Mexico State University, Las Cruces, New Mexico
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let be a completely regular Hausdorff space and C() the algebra of continuous real-valued functions on . In attempts to characterize abstractly those algebras that are isomorphic to C() for some , one produces subalgebras of C() which: (a) contain the constant functions, (b) separate points and closed sets in , (c) are closed under uniform convergence, and (d) are closed under inversion in C() (see, for example, (2; 5)).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 389 - 393
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Gillman, L. and Jerison, M., Rings of continuous functions (Princeton, 1960).10.1007/978-1-4615-7819-2CrossRefGoogle Scholar
2. Henriksen, M. and Johnson, D. G., On the structure of a class of archimedean lattice-ordered algebras, Fund. Math., 80 (1961), 73–94.Google Scholar
3. Henriksen, M., Johnson, D. G., and Isbell, J. R., Residue class fields of lattice-ordered algebras. Fund. Math., JO (1961), 107–117.10.4064/fm-50-2-107-117CrossRefGoogle Scholar
4. Hewitt, E., Certain generalizations of the Weierstrass approximation theorem, Duke Math. J., 15 (1947), 410–427.Google Scholar
5. Isbell, J. R., Algebras of uniformly continuous functions, Ann. of Math., 68 (1958), 96–125.Google Scholar
6. Mrόwka, S. G., Some approximation theorems for rings of unbounded functions, Amer. Math. Soc. Not., 11 (1964), 666.Google Scholar
7. Mrόwka, S. G., ƒunctionals on uniformly closed rings of continuous functions, Fund. Math., Ifi (1958), 81–87.10.4064/fm-46-1-81-87CrossRefGoogle Scholar