Date of Award

4-1968

Degree Type

Master's Essay - Restricted

Degree Name

Master of Science (MS)

Department

Mathematical and Statistical Sciences

Abstract

The notion of a convergent sequence of real numbers plays a basic role in the study of the real numbers. Although convergence has been used as the primitive notion for abstract spaces, some of its properties fail to hold in more general spaces than Hausdorff spaces. There are two concepts which can serve to generalize certain aspects of sequences, namely nets and filters. The need for a generalization of convergence of a sequence to a point in space developed early in the study of topology due to the fact that in topological spaces sequences cannot play the role that they play in Euclidean spaces. We will examine three propositions which illustrate ideas which are important in analysis but which are not true in general in topological spaces.

Comments

Submitted to the Department of Mathematics of Marquette University in partial fulfillment of the requirements for the degree of Master of Science. Milwaukee, Wisconsin

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