Topic: Convergence, Continuity and Completeness in Metric Spaces

Uniqueness and Basic Laws of Limits

The Sequential Criterion for Metric Continuity

Pointwise Epsilon-Delta Continuity

Piecewise Functions and Boundary Continuity

Open-Set Continuity for Metric Spaces

Metric-Space Convergence and Epsilon Balls

Lipschitz Maps and Continuity Bounds

Global Epsilon-Delta Continuity

Equivalence of Epsilon-Delta and Open-Set Continuity

Epsilon-Delta Estimates for Polynomial and Rational Maps