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Note on a Subalgebra of C(X)

Published online by Cambridge University Press:  20 November 2018

L. D. Nel  and
D. Riordan
L. D. Nel
Affiliation:
Carleton University, Ottawa, Ontario
D. Riordan
Affiliation:
Carleton University, Ottawa, Ontario
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C(X) (resp. C*(X)) will denote as usual the ring of all (resp. all bounded) continuous functions into the real line R. Define C#(X) to consist of all f∊C(X) whose image M(f) in the residue class ring C(X)jM is real for every maximal ideal M in C(X). Then C# shares with C* the property of being an intrinsically determined subalgebra of C. Then C* shares with C* the property of being an intrinsically determined subalgebra of C. The compactification corresponding to C# (as uniformity determining subalgebra of C*) is thus also an intrinsically determined one. We show that this compactification is well known and "natural" in the cases of several elementary spaces X.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 607 - 608
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Gillman, L. and Jerison, M., Rings of continuous functions, Van Nostrand, N.Y., 1960.Google Scholar