Compact Sets and Extreme Values

This lecture covers the concept of compact sets, extreme values, and the demonstration of theorems related to functions defined on these sets. The instructor revisits the fundamental theorem that every continuous function on a compact set is bounded and achieves its minimum and maximum values. The lecture progresses to demonstrate the concept of extreme values through examples and proofs. The importance of compactness in extracting extreme values from functions is highlighted, along with the significance of continuity in ensuring the existence of these values.