Day 229: Compactness in Metric Spaces

Learning Objectives

• •**Define** sequential compactness and total boundedness
• •**Prove** the equivalence of compactness conditions in metric spaces
• •**Apply** the Heine-Borel theorem in ℝⁿ
• •**State and use** the Arzelà-Ascoli theorem
• •**Understand** compact operators and their spectral properties
• •**Connect** compactness to approximation methods in quantum mechanics

Today's Schedule (7 hours)