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Answer to Question #2430 in Real Analysis for Ryan Weber

Question #2430
Let f:ℝ→ℝ be continuous on ℝ, and let P:={ x∈ℝ : f(x) > 0 }. If c∈P, show that there exists a neighborhood V_δ (c) ⊆ P
Expert's answer
The set P is an inverse image of the open interval (0, +∞). Since f is continuous, it follows from definition that P is open& in ℝ, whence every c from P has an open neighborhood V_c containing in P.

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