Spaces of valuations. Probability with a view toward statistics. Achim Jung dropped the countability condition and showed that there are two maximal cartesian closed categories of algebraic domains, bifinite domains and L-domains . Moreover, he proved that every cartesian closed category of algebraic domains is contained in one of these. For certain applications in semantic the more general class of continuous domains is considered rather than that of algebraic domains.
Continuous domains are exactly the retracts of algebraic domains.
Moreover, given a cartesian closed category of algebraic domains, the category comprising the retract of its objects is cartesian closed again. Take X the collection of all closed discs in the plane plus the plane itself. All other discs are mapped to the whole plane. S. Abramsky and A. Jung. Clarendon Press, 1994.