Topologies arising from metrics valued in abelian `-groups
نویسندگان
چکیده
This paper considers metrics valued in abelian `-groups and their induced topologies. In addition to a metric into an `-group, one needs a filter in the positive cone to determine which balls are neighborhoods of their center. As a key special case, we discuss a topology on a lattice ordered abelian group from the metric dG and the filter of positives consisting of the weak units of G; in the case of Rn, this is the Euclidean topology. We also show that there are many Nachbin convex topologies on an `-group which are not induced by any filter of the `-group.
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تاریخ انتشار 2010