定向完备偏序集上的模糊Scott拓扑

计算机工程与应用 ›› 2012, Vol. 48 ›› Issue (25): 57-60.

定向完备偏序集上的模糊Scott拓扑

路玲霞

石家庄经济学院数理学院，石家庄 050031

出版日期:2012-09-01 发布日期:2012-08-30

Fuzzy Scott topology on directed complete poset

LU Lingxia

School of Mathematics and Science, Shijiazhuang University of Econimics, Shijiazhuang 050031, China

Online:2012-09-01 Published:2012-08-30

摘要/Abstract

摘要： 设L是一个完备剩余格，定义了定向完备偏序集上的Hohle意义下的满层L-拓扑，称之为模糊Scott拓扑；基于满层的L-滤子，建立了相应的Scott收敛理论。证明了一个定向完备偏序集是连续的当且仅当对于每一个满层的L-滤子，其Scott收敛等价于按模糊Scott拓扑收敛。

关键词: 定向完备偏序集, 模糊Scott拓扑, 满层的L-滤子, Scott收敛

Abstract: Suppose that L is a complete residuated lattice, a stratified L-topology in sense of Hohle, called the fuzzy Scott topology, is defined on Directed Complete Poset（DCPO）. Based on stratified L-filters, the corresponding Scott convergence theory is established. It is shown that a DCPO is continuous iff for any stratified L-filter, Scott convergence coincides with convergence about the fuzzy Scott topology.

Key words: Directed Complete Poset（DCPO）, fuzzy Scott topology, stratified L-filter, Scott convergence

路玲霞. 定向完备偏序集上的模糊Scott拓扑[J]. 计算机工程与应用, 2012, 48(25): 57-60.

LU Lingxia. Fuzzy Scott topology on directed complete poset[J]. Computer Engineering and Applications, 2012, 48(25): 57-60.