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Math and science::Analysis

Exercise: nested sequences of sets

The following statement is [true or false?]

If \( F_1 \supseteq F_2 \supseteq F_3 \supseteq F_4 \supseteq ... \) is a nested sequence of nonempty closed sets, then the intersection \( \bigcap_{n=1}^{\infty} F_n \neq \emptyset \).