Topic: Convergence, Continuity and Completeness in Metric Spaces

Discontinuity Tests Using Sequences

Detecting Incompleteness with Cauchy Sequences

Coordinatewise Convergence and Completeness of Rn

Convergent Sequences Are Cauchy

Continuity of Sums, Products, and Quotients

Completeness of Bounded Functions in the Sup Metric

Completeness of the Real Line

Completeness and Its Metric Examples

Common Errors in Metric Convergence and Continuity

Cauchy Sequences and Their Basic Estimates