#### Degree Name

Master of Science

#### Department or Program

Mathematics

#### Advisor

Joseph Hundley

#### Abstract

In this paper we find basis for a specific vector space that we will introduce later on. In chapter 1, we make a general review of some abstract algebra and topology. In chapter 2, we define the absolute value on a field in general and we introduce a new type of absolute values called the p- adic absolute value. In chapter 3 we define some vector space and we get a good understanding of its elements. Finally, in chapter four, we define a subspace of the vector space defined in chapter 3 and we find basis for this subspace.