Let (Kn n N) be a sequence of nonempty compact sets in R such that K1 K2 Kn Prove that there exists at least one point x R such that x Kn for all n N, that is, the intersection is not empty Kn

Question: Let (Kn : n N) be a sequence of nonempty compact sets in R such that K1 K2 Kn . Prove that there exists at

Let (Kn : n ˆˆ N) be a sequence of nonempty compact sets in R such that K1 Šƒ K2 Šƒ ˆ™ ˆ™ ˆ™ Kn Šƒ ˆ™ ˆ™ ˆ™. Prove that there exists at least one point x ˆˆ R such that x ˆˆ Kn for all n ˆˆ N, that is, the intersection is not empty.

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