Geodesic
A Note on Strongly Regular Function Algebras
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 912-914

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

Let A be a uniformly closed subalgebra of C(X), the algebra of all complex-valued continuous functions on a compact Hausdorff space X. If A separates the points of X and contains the constant functions, A is called a function algebra. The algebra A is said to be strongly regular on X if it has the following property. Property. For each f in A, each point x in X, and every , there is a neighbourhood U of x and a function g in A with g(y) = f(x) for all y in U and for all y in X.That is, each function in A is uniformly approximate on X by functions in A which are constant near any point of X. Stated in terms of ideals, strong regularity means that, for each x, the ideal of functions vanishing in a neighbourhood of x is uniformly dense in the maximal ideal at x. 
Wilken, Donald R. A Note on Strongly Regular Function Algebras. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 912-914. doi: 10.4153/CJM-1969-100-0
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