Strongly continuous posets and the local Scott topology (Q932355)

The concept of a strongly continuous poset is defined. Four notions of continuity on posets are compared. The main results are: {\parindent=5mm \begin{itemize}\item[1)] A poset is strongly continuous iff its local Scott topology is equivalent to its Scott topology and is completely distributive iff it is a continuous precup. \item[2)] For precups, the four studied notions of continuity are equivalent, although they disagree on arbitrary posets. \item[3)] A \(T_0\)-space is a strongly continuous poset equipped with a Scott topology iff this space is weakly monotone convergent and has a distributive topology that is contained in the local Scott topology of the specialization order. \end{itemize}}