Publisher Summary This chapter defines topological spaces and the related theorems. The condition for a set A to be open in a metric space is that each point of A belongs to an open ball contained in A. A space that contains no other closed-open subset is called connected. The union of two closed sets is a closed set. This theorem can be generalized by induction to an arbitrary finite number of sets. The chapter also presents the theorems that states that the intersection of an arbitrary number of closed sets is a closed set and that the intersection of a finite number of open sets is an open set.