Let C0=[0,1]. Cn is obtained by removing the middle open interval of length α/3n from each...

Let C₀=[0,1]. C_n is obtained by removing the middle open interval of length α/3ⁿ from each interval of C_n-1 where α∈(0,1).

Let C=⋂C_n. Prove that C contains only boundary points, i.e., x∈C is a boundary point of C if every neighborhood of x contains at least one point in C and at least one point not in C.

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Colby Messinger answered 2 hours ago

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