Proving Disconnectedness in Sets: Closed and Open/Closed Cases

[jessicaw]

Homework Statement

union of 2 disjoint sets is disconnected

Homework Equations

The Attempt at a Solution

For open disjoint sets it is obvious as it is the definition of disconectedness.
So it remains to prove the closed sets/one open and open closed set case.
In any case, i draw some diagrams and i believe they are disconnected.

 

[Dick]

Homework Statement

union of 2 disjoint sets is disconnected

Homework Equations

The Attempt at a Solution

For open disjoint sets it is obvious as it is the definition of disconectedness.
So it remains to prove the closed sets/one open and open closed set case.
In any case, i draw some diagrams and i believe they are disconnected.

Think hard about the one open/one closed case.