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Prove that T, the set of rationals in U1 , is not a connected subset of U1 . Let I be any family of connected subsets of a metric 6 space X such...
21. Prove that T, the set of rationals in U1 , is not a connected subset of U1 . 22. Let I be any family of connected subsets of a metric 6 space X such that any two members of I have a common point. Prove that F is connected. 23. Prove that if S is a connected subset of a metric space, then S is connected. 24. Prove that any interval I t U1 is a connected subset of U1 . 25. Prove that if A is a connected set in a metric space and A t B t A, then B is connected. Fn * 1 be a nested sequence of compact sets, each of which is conn * ? nected. Prove that Fn is connected.
