A Characterization Of Quasicontinuous Posets By Nets

This dissertation introduces the concept of(quasi)liminf convergence in posets by means of cut operator.Some properties of them are investigated.It is proved that(1)A poset P is τ-continuous iff the S-convergence is topological iff it is meet τcontinuous and the liminf convergence is topological.(2)A poset is a τquasicontinuous poset iff the GS-convergence is topological.(3)A poset which is meet τ-continuous is τ-quasicontinuous poset iff the quasiliminf convergence is topological.