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Real Analysis : Connectedness and Convergent Sequence

Show that A set E subset or equal to R is connected if and only if, for all nonempty disjoint sets A and B satisfying E=A U B there always exists a convergent sequence (x_n)-->x with (x_n) contained in one of A or B and x an element of the other.

Solution Summary

The relationship between connectedness and a convergent sequence is investigated. The solution is detailed and well presented.

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