L-拟序集中的层次收敛与完备性

Stratified-convergence and completion on L-Preordered sets

研究了L 拟序集中的层次收敛与完备性 .在L 拟序集上引入了三种关系 ,并讨论了它们之间的关系及性质 ;定义了Cauchy网及层次Cauchy网 ,从而把Cauchy列与层次Cauchy列的概念推广到了网的水平 .证明了序列的层次极限的等价刻画对网的层极限仍适用 ,并给出了层次Cauchy网的层极限的一个重要性质 ,得到了偏序集和Frame作为L

The stratified convergence and completion on L Preordered sets are discussed. Three relations on the L Preordered sets are introduced and their properties are given at the beginning. The main part of this paper is to generalize Cauchy sequences to Cauchy nets and stratified Cauchy sequences to stratified Cauchy nets and characterizes the properties of stratified limit in this case. Finally two important results about the completion on two special cases are given.