Compactness and its applications

Thumbnail Image
October 18, 2016
Journal Title
Journal ISSN
Volume Title
In this study, we explore the concept of compactness as a core of general topology. Compactness together with Continuity and Connectedness form the so called 3 Cs of general topology. We delve into some of the useful theorems in general topology before singling out the less intuitive topic of compactness touching on almost every aspect of the topic. This work does not shy away from the usefulness of compactness in mathematical analysis and hence explains its application therein. The study nally looks at an example of the applications of compactness in a real life situation.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology In partial fulfillment of the requirement for the Degree of Master of Philosophy in Pure Mathematics,