量化Domain中的反向层次收敛

Backward-Convergence with respect to A Testing Sequence in the Quantitative Domain

在LF-拟序集中引进了反向层次收敛理论.给出了反向层次收敛序列的性质和若干等价条件,得出了经典序伴随理论中一个重要性质的层次化版本.此外,还引进了紧性和全有界性等概念,它们是度量空间中相应概念在LF-伪序集中的对应形式.最后研究了可变层次结构的若干性质.

This paper investigates backward-convergence theory with respect to a testing sequence. Backward-convergence with respect to a testing sequence is introduced and its properties and sufficient and necessary condition are presented. In addition, It obtains a new form of an important property in adjoint theory. The concepts of compactness and totally bounded property in LF-pseudo ordered sets are also introduced, which are correspondent to compactness and totally bounded property in metric spaces. At last, it discusses properties of variable testing sequences.