Homework 17: Compactness

1. Section 7.1, #7.8, 7.9, 7.13(a).
2. Prove that \(X\) is compact if and only if the following condition holds: For every collection \(\cC\) of closed sets in \(X\) whose itersection is empty, there exists a finite subcollection of \(\cC\) whose intersection is empty.
   Note: You may find it helpful to solve this problem before solving the textbook problems above.