A quick construction of a retraction of all retractions for stable bifinites (Q1891153)

A cpo is a directed-complete partial order with least element. A meet cpo is a cpo with a binary operation, meet, that is defined for pairs of elements with an upper bound and distributes over directed joins. A map between meet cpo's is stable if it is continuous and distributes over meets (whenever defined). A stable bifinite \(D\) is a meet cpo with a directed set of stable functions from \(D\) to \(D\) that have finite images and join to the identity map under a special ordering of stable maps. This paper is devoted to a simple short proof that the collection of stable retractions over a stable bifinite \(D\) is a retract of its stable functional space \(D \to D\).