The Patch Construction is Dual to Algebraic DCPO Representation

@article{Townsend2011ThePC,
  title={The Patch Construction is Dual to Algebraic DCPO Representation},
  author={Christopher F. Townsend},
  journal={Applied Categorical Structures},
  year={2011},
  volume={19},
  pages={61-92}
}
Using the parallel between the preframe and the suplattice approach to locale theory it is shown that the patch construction, as an action on topologies, is the same thing as the process of recovering a discrete poset from its algebraic dcpo (ideal completion).