title: Convergence in [Formula: see text]-quasicontinuous posets.
abstract: In this paper, we present one way to generalize [Formula: see text]-convergence and [Formula: see text]-convergence of nets for arbitrary posets by use of the cut operator instead of joins. Some convergence theoretical characterizations of [Formula: see text]-continuity and [Formula: see text]-quasicontinuity of posets are given. The main results are: (1) a poset P is [Formula: see text]-continuous if and only if the [Formula: see text]-convergence in P is topological; (2) P is [Formula: see text]-quasicontinuous if and only if the [Formula: see text]-convergence in P is topological.
authors.affiliation: Department of Mathematics, Sichuan University, Chengdu, 610064 Sichuan People's Republic of China.|Department of Mathematics, Nanchang University, Nanchang, 330031 Jiangxi People's Republic of China.
authors.forename: Xiao-Jun
authors.initials: XJ
authors.lastname: Ruan
authors.affiliation: College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022 Jiangxi People's Republic of China.
authors.forename: Xiao-Quan
authors.initials: XQ
authors.lastname: Xu
keywords: Weak Scott topology; [Formula: see text]-Continuous poset; [Formula: see text]-Convergence; [Formula: see text]-Quasicontinuous poset