Date of Award


Document Type


Degree Name

Master of Science

Degree Discipline



Many of the ideas of mathematics have come about because of certain properties of the real numbers. Some of these are convergence, metric spaces, abstract measure theory, and topology.

Because of the beauty and interest of the real number system, it is the most used "concrete" example to express the abstract ideas in a mathematical system. Set theory is another important tool in modern mathematics. Most of our important concepts in modern mathematics are based on set theory. In this paper, we examine some properties shared by both the real numbers and subsets of a given set.

The theorems presented will relate to three areas of mathematics namely, analysis and limiting processes, algebra and partially ordered spaces and topology. The paper begins with definitions and notations. Chapter II includes pre^ liminary theorems and lemmas. Chapter III contains a series of theorems shared by the real numbers and subsets of a given set. We conclude with chapter IV, which relates some algebraic and topological properties of subsets of X.

Committee Chair/Advisor

Willie Taylor

Committee Member

Freddie Frazier


Prairie View Agriculture And Mechanical College


© 2021 Prairie View A & M University

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Date of Digitization


Contributing Institution

John B Coleman Library

City of Publication

Prairie View





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