Math 131 Lecture 11 021224 Compact Sets part 2

More facts about compact sets. Any closed subset of a compact set is compact. Any collection of compact sets that satisfies the finite intersection property has a nonempty intersection. Compact implies limit point compact: any infinite subset of a compact set must have a limit point in the compact set. Any set of nested closed and bounded intervals has a nonempty intersection (similarly for k-cells). K-cells are compact.