1. Using the definition of an open set, prove that the subset S=(a1,b1)X(a2,b2) of the Euclidean space R2 is open.

2.Let S ⊂ R$\displaystyle n$ be a compact set and let y ∈S$\displaystyle c$ . Prove that there exists a strictly

positive number d such that //x − y// ≥ d , for any x∈ S

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