Category Archives: Dense

February 1998 #1

Problem Statement: Let be an uncountable collection of open sets in . Let . Prove there exists a countable collection of open intervals satisfying (1) and (2) for every positive integer there exists an such that . Proof: Since the rationals are … Continue reading

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May 1990 #3

Problem Statement: For , let denote the set of cluster points of . Show there exists no set such that . Proof: Suppose that there is a set such that . Let such that is irrational. Let and consider the … Continue reading

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