格L中点式拟度量的研究

Research of Pointwise Quasi-metric in L Lattice

本文证明了在格L中点式拟度量中分别借助远域和邻域能够刻画两种不同拓扑,并进一步证明了该度量须满足连续性公理的条件时这两种拓扑等价.最后借助一个给定的点式拟度量能构造出一个新的Erceg-Peng度量且对相关的性质进行了讨论.

In this paper,we show that two kinds of different topologies are respectively charactered by far fields and neighborhood fields in pointwise quasi-metric on L lattice,and further prove that if the measure still satisfies the continous law,then these two kinds of topologies are equivalent.At last,according to a pointwise quasi-metric given,we can construct a new Erceg-Peng metric and discuss some their related properties.