Day 226: Convergence and Continuity in Metric Spaces

Learning Objectives

• •**Define and verify** convergence of sequences in metric spaces
• •**Characterize** open balls, open sets, and closed sets topologically
• •**Prove** continuity using both sequential and ε-δ definitions
• •**Understand** the relationship between metric and topological structures
• •**Apply** continuity to linear operators on normed spaces
• •**Connect** convergence concepts to quantum mechanical state evolution

Today's Schedule (7 hours)