# Real Analysis : Connected and Disconnected Sets

Not what you're looking for? Search our solutions OR ask your own Custom question.

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?

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:05 pm ad1c9bdddfhttps://brainmass.com/math/real-analysis/real-analysis-connected-and-disconnected-sets-27562

#### 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.

b.

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

#### Solution Summary

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

$2.49