QFS-domains and quasicontinuous domains. (Q2355457)

In domain theory difficulties with cartesian closedness are well-known, namely the category of continuous domains and Scott-continuous functions is not cartesian closed. Identifying maximal cartesian closed subcategories is a subtle matter which gave rise to the notions of RB-domains and FS-domains, and further to quasicontinuous domains, QRB-domains, and QFS-domains. In this article the notion of \(\omega\)QFS-domain is given, and in a short series of results it is shown that for a QFS-domain, \(\omega\)QFS is equivalent to the existence of a countable base for the Scott topology, that Scott-continuous retracts of QFS-domains are QFS-domains, that Lawson compactness for a quasicontinuous domain is determined by a certain condition on upper sets, and that QFS-domains are quasicontinuous domains together with a certain separating condition.