Geodesic
Algebras of Holomorphic Functions in Ringed Spaces, I
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1281-1292

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

A pair () is a ringed space if it is a subsheaf of rings with 1 of the sheaf of germs of continuous functions on X. If U is an open subset of X, we denote the set of sections over U relative to by . If , then implies that there exists some open neighbourhood V of u, V ⊂ U, and some g continuous on V such that the germ of g at u, ug is φ(u). Now we define φ(u) (u) to be g(u) and in this way we obtain, in a unique fashion, a continuous complex-valued function on U. The collection of all such functions for a given set is denoted by and is called the -holomorphic functions on U.THEOREM. Let X be a locally connected Hausdorff space and () a ringed space. 
Shauck, Maxwell E. Algebras of Holomorphic Functions in Ringed Spaces, I. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1281-1292. doi: 10.4153/CJM-1969-141-8
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