Abstract
This chapter presents some surprising base properties in topology II. The base properties of the sort surveyed in [N1] fall into two general categories: (1) those involving conditions under which an intersection of open sets is open and (2) those that involve partial order relations between members of the base. The first section has to do with non-Archimedean spaces, which form the intersection of these two kinds of properties. A space is called non-Archimedean if it has a rank 1 base. It has a base B such that the collection B(x) of all members of B containing a point x is totally ordered by containment for every point x. This is the order aspect of non-Archimedean spaces.
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