Connectedness

A connected space is a topological space which consists of a single piece and is considered one of the simplest properties which such a space may possess and one of the most important for the applications of topology to analysis and geometry. Connectedness is also a basic notion in complex analysis, for the regions on which analytic functions are studied are generally taken to be connected open subspaces of the complex plane. The concept of connectedness is important in the measurement of the degree of relationship between the members of a social group.