An Alternative Definition of the Completion of Metric Spaces

Cheng Hao

Published 2008-10-05, updated 2011-12-03Version 3

In this article, the author proposes another way to define the completion of a metric space, which is different from the classical one via the dense property, and prove the equivalence between two definitions. This definition is based on considerations from category theory, and can be generalized to arbitrary categories.