Θ-continuity and Dθ-completion of posets. (27th February 2017) - ZHANG, ZHONGXI; LI, QINGGUO; JIA, XIAODONG
Abstract : We introduce a new concept of continuity of posets, called θ-continuity. Topological characterizations of θ-continuous posets are put forward. We also present two types of dcpo-completion of posets which are D θ -completion and Ds2 -completion. Connections between these notions of continuity and dcpo-completions of posets are investigated. The main results are (1) a poset P is θ-continuous iff its θ-topology lattice is completely distributive iff it is a quasi θ-continuous and meet θ-continuous poset iff its D θ -completion is a domain; (2) the D θ -completion of a poset B is isomorphic to a domain L iff B is a θ-embedded basis of L ; (3) if a poset P is θ-continuous, then the D θ -completion D θ ( P ) is isomorphic to the round ideal completion RI ( P, ≪θ ).