AN EPISTEMOLOGICAL ANALYSIS OF COMPACTNESS IN ANALYSIS AND TOPOLOGY

Abstract

Compactness in metric and topological spaces is one of the basic concepts of Topology. It is a property that generalizes the notion of a subset of Euclidean space being closed and bounded. Many of the concepts in the Topology as well as in the metric space are based on this concept. This paper presents an epistemological analysis that clarifies the emergence and development of the concept of compactness and determines the epistemological characteristics of these two knowledge objects.