Quasi-liminf convergence in posets.

In this paper, the concepts of g s 2 -convergence and quasi-liminf convergence of filters in posets are introduced. The main results are: (1) For an order consistent topology τ on a poset P , P is τ -quasicontinuous iff the g s 2 -convergence coincides with τ -convergence; (2) For an order consistent topology τ on a poset P , the quasi-liminf convergence coincides with τ ∨ ω (P) -convergence if P is τ -quasicontinuous; (3) For an order consistent topology τ on a poset P , P is τ -continuous iff the s 2 -convergence coincides with τ -convergence iff it is meet τ -continuous and the quasi-liminf convergence coincides with τ ∨ ω (P) -convergence. [ABSTRACT FROM AUTHOR]