Connectedness

A topological space is said to be connected if it is not the union of two disjoint nonempty open sets.

Graph theory also offers a context-free measure of connectedness, called the clustering coefficient.

Other fields of mathematics are concerned with objects that are rarely considered as topological spaces.

We might wish to call a topological space connected if each pair of points in it is joined by a path.

Properties and parameters based on the idea of connectedness often involve the word connectivity.

While terminology varies, noun forms of connectedness-related properties often include the term connectivity.

On the other hand, in fields without a formally defined notion of connectivity, the word may be used as a synonym for connectedness.