Solution-Discuss topic-preservation of sign

Discuss topic-preservation of sign

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Question: Preservation of sign. Let be a continuous function from a metric space (X, d) to R, with the usual metric. Prove (directly) that the set {x ∈ X; (x) > 0} is open. Intuitively, this result says that a continuous function that is strictly positive (or negative) at a point will maintain its sign within a sufficiently small ball around the original point.

Reference no: EM131582634

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Discuss topic-preservation of sign : Preservation of sign. Let be a continuous function from a metric space (X, d) to R, with the usual metric. Prove (directly) that the set {x ? X; (x) > 0}.

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Discuss topic-preservation of sign

Reference no: EM131582634

Reference no: EM131582634

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