The object of this thesis is to examine properties of an abstract vector space of finite dimension n. The properties of the set of complex numbers are assumed, and the definition of a field and of an abelian group are not stated, although reference to these systems is made.

This thesis explores the fundamental properties of the contingent.

The purpose of this paper is to present the results of a study of linear spaces with special emphasis of linear transformations, norms, and inner products.

Axioms for a topological space are generally based on neighborhoods where "neighborhood" is an undefined term. Then, limit points are defined in terms of neighborhoods. However, limit points seem to be the basic concept of a topological space, rather than neighborhoods. For this reason, it will be attempted to state a set of axioms for a topological space, using limit point as the undefined concept, and to delete the idea of neighborhoods from the theory.

This thesis investigates some of the properties of certain transformations. Some properties are considered in general; others, only in the xy-plane.