Geodesic
A Functional Analytic Description of Normal Spaces
Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 45-49

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Throughout the paper, X will denote a completely regular (Hausdorff) topological space and C(X) the R-algebra of all real-valued continuous functions on X. When this algebra carries the continuous convergence structure [1], we write CC (X). We note that C C(X)is a complete [5] convergence R-algebra [1].Our description of normality reads as follows. A completely regular topological space X is normal if and only if CC (X)/J (endowed with the obvious quotient structure; see § 1) is complete for every closed ideal J ⊂ CC (X). 
Binz, E.; Feldman, W. A Functional Analytic Description of Normal Spaces. Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 45-49. doi: 10.4153/CJM-1972-006-9
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