Explore BrainMass

Explore BrainMass

    Real Analysis : Connected and Disconnected Sets

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

    A- Find an example of a disconnected set whose closure is connected.

    b- If A is connected ,is A closure necessarily connected? If A is perfect is A closure necessarily perfect?

    © BrainMass Inc. brainmass.com March 4, 2021, 6:04 pm ad1c9bdddf

    Solution Preview

    a. Q is the set of rational numbers. It is obviously a disconnected set because we can find an irrational number a, such that Q is contained in the union of the two disjoint open sets (-inf,a) and (a,inf). Because Q is dense in R, so the closure of Q is R, which is connected.

    (1) Yes. If A is connected, the A ...

    Solution Summary

    Connected and Disconnected Sets and Closure are investigated. The solution is detailed.