A study of convergences in partially ordered sets

In this paper we obtain alternative proofs of the fact that the ideal-o2-convergence in a poset is topological if and only if the poset is O2-doubly continuous. We also introduce and study the ideal-lim-inf-convergence in a poset, exploiting the relation between the induced ideal-lim-inf-topology, lim-inf-topology and Scott topology. Finally, we give a necessary and sufficient condition in order the ideal-lim-inf-convergence to be topological.