Equivalence of Metrics is not Defined/Mistake

Source Work

 * Part $\text I$: Basic Definitions
 * Section $5$. Metric Spaces
 * Complete Metric Spaces
 * Complete Metric Spaces

Mistake

 * The concept of equivalence of metrics is not defined, although the concept is mentioned and used in the context of complete metric spaces.

Equivalent Metrics
The definition is as follows: