Explore BrainMass

Explore BrainMass

    Real Analysis : Connectedness and Convergent Sequence

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com February 24, 2021, 2:32 pm ad1c9bdddf
    https://brainmass.com/math/real-analysis/27430

    Solution Summary

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

    $2.19

    ADVERTISEMENT