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

• 研究、探讨 • 上一篇    下一篇

定向完备偏序集上的模糊Scott拓扑

路玲霞   

  1. 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   

  1. School of Mathematics and Science, Shijiazhuang University of Econimics, Shijiazhuang 050031, China
  • Online:2012-09-01 Published:2012-08-30

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