A set A is called clopen if and only if it is both open and closed. a)
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a) Prove that every Euclidean space has at least two clopen sets.
b) Prove that a proper subset E of Rn is connected if and only if it contains exactly two relatively clopen sets.
c) Prove that every nonempty proper subset of Rn has a nonempty boundary.
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a By Remark 823 and R n are clopen b Suppose A is clopen and A ...View the full answer
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