Connected space

In topology, a connected space is a fundamental concept that refers to a topological space that cannot be divided into two disjoint, non-empty open sets. More formally, a topological space \( X \) is called connected if there do not exist two open sets \( U \) and \( V \) such that: 1. \( U \cap V = \emptyset \) 2. \( U \cup V = X \) 3.