伪度量族与一致结构格集的关系及格集之并的性质

Relations between Family of Pseudo-metrics and Gage of Uniformity and Properties on Union of Gages

给出非空集X的伪度量族P为格集的一个充分必要条件,构造使P不为格集的反例,并讨论由格集之并所生成的一致结构的性质.

The necessary and sufficient condition for a family P of pseudo-metrics for non-empty set X to be a gage is given,some counterexamples for P not to be a gage are constructed,and the property of uniformity generated by union of gages is discussed.