Chapter 7.2, Problem 10E

(a)

To determine

To Prove: That ${\displaystyle \underset{A\in ƛ}{\cap }A}$ is a closed set.

(b)

To determine

To Prove: That ${\displaystyle \underset{A\in ƛ}{\cup }{A}^c}$ is a closed set, when $ƛ$ is a finite collection.

(c)

To determine

To find: The example that ${\displaystyle \underset{A\in ƛ}{\cup }{A}^c}$ is not a closed set when $ƛ$ is a finite collection.