Theorem Let S be a convex set in R" with a nonempty interior. Let x₁ = cl S and X2 € int S. Then 2x₁ +(1-2)x₂ = int S for each 1 € (0,1).
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![Theorem
Let S be a convex set in R" with a nonempty interior. Let x₁ = cl S and x₂ = int
S. Then 2x₁ +(1-2)x₂ = int S for each λ = (0,1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde96565d-a00c-4ce3-89c1-68d207bd36b0%2F62274ba0-3abb-4e20-ab3f-71aafa5b76f2%2Fwryqw4v_processed.jpeg&w=3840&q=75)
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