Suppose that E is a bounded noncompact subset of Rn and that f E (0, ) If there is a g E R such that g(x) f(x) for all x E, then prove that there exist x1, , xN E such that E UBgx)

Question: Suppose that E is a bounded noncompact subset of Rn and that f: E (0, ). If there is a g: E R such that

Suppose that E is a bounded noncompact subset of Rn and that f: E †’ (0, ˆž). If there is a g: †’ E †’ R such that g(x) > f(x) for all x ˆˆ E, then prove that there exist x1,..., xN ˆˆ E such that

E UBgx)

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