A completion of a metric space $(M,d)$ is a complete metric space $(M^*,d^*)$ such that $(M,d)$ is a dense subspace of $(M^*,d^*)$. I understand this, but how do I explicitely find a completion of a given space?
I need to find the completion of the non complete metric space of real valued compact supported continuous functions with sup norm but I have no idea on how to. I already proved that the space is not complete using the hints in these two answers:
Is the set of all real valued continuous functions on $\mathbb R$ with compact support complete?
Completeness of continuous real valued functions with compact support
Thanks.