Rational Extensions of C(X) via Hausdorff Continuous Functions
Anguelov, Roumen
Original · EN
The ring operations and the metric on C(X) are extended to the set Hnf(X) of all nearly finite Hausdorff continuous interval valued functions and it is shown that Hnf(X) is both rationally and topologically complete. Hence, the rings of quotients of C(X) as well as their metric completions are represented as rings of Hausdorff continuous functions.
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