Hegel and Modern Topology

Abstract: In this paper we show how some fundamental concepts of modern topology can be understood philosophically in the light of Hegel's Logic as well how modern topological concepts can provide concrete illustrations of many of the concepts and deductions that Hegel used. This paper can be seen as a continuation of our paper \cite{pro} where we argued that the prototypes of many fundamental notions of modern topology were already found in Aristotle's Physics. This paper is divided into two parts. The first part (sections 2 - 9) focuses only on elementary topology while the remaining sections discuss advanced category theory.