抄録
It is well known that the meaning of the convergence in posets stings the
interest of many investigators such as R. F. Anderson, J. C. Mathews and V. Olej˘cek
(see, for example [13,14]). Among others, the notions of the order-convergence and of
the o2-convergence in posets were studied in details, presenting necessary and sufficient
conditions under of which these convergences are topological. Many researchers give a
special attention to the study of these convergences in different posets, inserting new
knowledge in the classical theory of posets’s convergence. In this paper, we introduce
the ideal-order-convergence in posets, proving results which are based on this notion.
We insert topologies in posets and we study their properties. We also give a sufficient
and necessary condition for the ideal-order-convergence in a poset to be topological.
The introduction of a weaker form of the ideal-order-convergence in posets, called
ideal-o2-convergence, completes our study.
