Geodesic
Note on a Subalgebra of C(X)
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 607-608

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Nel, L. D.; Riordan, D. Note on a Subalgebra of C(X). Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 607-608. doi: 10.4153/CMB-1972-108-4
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[1] 1. Gillman, L. and Jerison, M., Rings of continuous functions, Van Nostrand, N.Y., 1960. Google Scholar

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