Completion of Metric Spaces - 16

In this lecture, we prove that any metric space (X,d) has a completion (X*,d). We take inspiration from our in-class construction of the real numbers from the rational numbers using equivalence classes of Cauchy sequences, and we generalize this approach.

Pre-Lecture Materials

Completion of metric spaces: Pre-lecture video A

Completion of metric spaces: Pre-lecture video B

In-Class Activities

Open the following Overleaf link and make a copy for yourself. Remember to include the names of everyone who worked together in the document.

Lecture 16 In-Class Activity: Completing a Metric Space

Assignments

  • Submit Overleaf Proof 16: Completion of Metric Spaces
  • Homework 8

Additional Materials

Lecture Notes