  Compact sets in constructive mathematics capture our intuition of what
computable subsets of the plane (or any other complete metric space) ought to
be. A good representation of compact sets provides an efficient means of
creating and displaying images with a computer. In this paper, I build upon
existing work about complete metric spaces to define compact sets as the
completion of the space of finite sets under the Hausdorff metric. This
definition allowed me to quickly develop a computer verified theory of compact
sets. I applied this theory to compute provably correct plots of uniformly
continuous functions.
