Abstract
Let A be a topological ring. If S is a multiplicatively closed subset of A, we define a natural topology on the localization (or ring of fractions) A S of A with respect to S. The ring A S endowed with this topology is said to be the topological localization of A with respect to S, and it is characterized by a universal property. Let X be a topological space and let C ( X) be the topological ring of all K -valued continuous functions on X K = R or C ) endowed with the compact-open topology. If U is a cozero-set in X, we obtain that the topological ring C ( U) coincides with the topological localization of C ( X) with respect to S = {ƒ ϵ C ( X): 0 ∉ ƒ( U)}.
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