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Stratified convergence and completion on \(L\)-preordered sets. (Chinese. English summary) Zbl 1023.06008

Summary: 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. The main object of this paper is to generalize Cauchy sequences to Cauchy nets and stratified Cauchy sequences to stratified Cauchy nets, and to characterize the properties of stratified limits in this case. Finally two important results about completion in two special cases are given.

MSC:

06B35 Continuous lattices and posets, applications
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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