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A Positivstellensatz For Rings Of Continuous-Functions

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1987

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Elsevier Science
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A one page proof (using the real spectrum) of the following result: Let f, g : X ! R be a continuous functions on a topological space X, such that f is strictly positive on g−1(0). Then there exist continuous functions u, v and w such that (1 + v2)f = 1 + w2 + gu.

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