Characteristics of infinite dimensional vector spaces

Abstract

The study of finite dimensional vector spaces has been logically extended to that of infinite dimensional vector spaces. Of fundamental importance to this study is the relationship between sets which span a vector space, basis sets for such a space, and linearly independent sets within the space. Without recourse to the finite dimensional case, a new proof is presented to show this relationship. A corollary to this is the most important result that every basis for a vector space has the same cardinal number.http://www.archive.org/details/characteristicso00wellMajor, United States Marine Corp