Knijnenburg’s dcpo, weakly Hausdorff spaces and lenses

In 1993, Knijnenburg studied lenses, and came up with a simple dcpo that shows that the topological and the ordinary Egli-Milner orderings on lenses can differ. This dcpo settles more than this question. For example, it is an algebraic dcpo that is neither coherent nor weakly Hausdorff. It has a lens whose closure differs from its downward closure, and it is a projective limit of weakly Hausdorff spaces that is not weakly Hausdorff, as we will see in the full post.