ξ-closed subsets and rings of fractions of C(X)
First, multiplicative closed ξ-subsets of a commutative ring are defined. Next, multiplicative closed ξ-subsets of C(X) which are saturated are characterized. Finally, for a multiplicative closed ξsubset S of C(X) and its associated filter FS of subsets of X generated by cozero-sets of elements of S it is shown that two rings S −1C(X) and the ring of direct limits of continuous functions on members of FS are isomorphic.
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