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(Solved): 12.1. Definition. A Set S Is Connected If It Cannot Be Separated By Two Disjoint Open Sets U1 And U2...


12.1. Definition. A set S is connected if it cannot be separated by two disjoint open sets U1 and U2 into two nonempty piecesProve from the definition (Definition 12.1) that the rational numbers Q are disconnected.

12.1. Definition. A set S is connected if it cannot be separated by two disjoint open sets U1 and U2 into two nonempty pieces Sn Ui and Sn U2 (such that S= (s nU) U (SAU2)). Prove from the definition (Definition 12.1) that the rational numbers Q are disconnected.


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