Characterization of compact metric spaces in terms of Cantor set

Abstract

The Cantor set is a fundamental construct in mathematics that has been extensively studied for its interesting properties and applications in various fields. On the other hand, a metric space is a set together with a notion of distance between its elements, usually called points. Metric spaces are the most general setting used for understanding many of the concepts of mathematical analysis and geometry. The aim of this thesis is to explore the relationship between the Cantor set and compact metric spaces.