Some Basic Results in ν-Normed Spaces

Abstract

In this paper, we introduce the notion of a directed preserving generator (d.p.g.) from R into R. This d.p.g. can be used to construct new fields which generally have the same properties as R, except that some properties are affected by d.p.g. itself. With this new field, a ν-normed space will be formed. Some of the basic properties of this normed space are also discussed.