Is there any Cartesian-closed category of continuous domains that would beclosed under Jones and Plotkin's probabilistic powerdomain construction? Thisis a major open problem in the area of denotational semantics of probabilistichigher-order languages. We relax the question, and look for quasi-continuousdcpos instead. We introduce a natural class of such quasi-continuous dcpos, theomega-QRB-domains. We show that they form a category omega-QRB with pleasingproperties: omega-QRB is closed under the probabilistic powerdomain functor,under finite products, under taking bilimits of expanding sequences, underretracts, and even under so-called quasi-retracts. But... omega-QRB is notCartesian closed. We conclude by showing that the QRB domains are just one halfof an FS-domain, merely lacking control.
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