Day 225: Metric Spaces — Definitions and Examples

Learning Objectives

• •**State and verify** the three axioms defining a metric space
• •**Compute distances** in ℝⁿ with Euclidean, taxicab, and supremum metrics
• •**Define and work with** sequence spaces l^p for p ∈ [1, ∞]
• •**Understand** the function spaces C[a,b] and L^p with their natural metrics
• •**Prove** that a given distance function is (or is not) a valid metric
• •**Connect** metric space structure to quantum mechanical state spaces

Today's Schedule (7 hours)