Partial Order O_M- Convergence And Convergence Liminf- Set

In this thesis, we investigate convergence properties on posets as follows:The first part of this thesis, we introduce a new definition of con-vergence. The main results one is OM-convergence based on the O2-convergence for poset. Then we discuss some basic properties of OM-convergence. Specially, we prove that OM-convergence on a poset P is topological if and only if the P is double α(M)-continuous. Fi-nally, we investigate some properties of the lim inf2-convergence for a poset P.On the second part, we investigate some properties of the lim inf-convergence for a dcpo. A sufficient and necessary condition for lim inf-convergence to be topological is given. Finally, we investi-gate the relationship between the category DCPO and the category CONV.