adj. 1. (of a relation) such that either it or its converse holds between any two members of the domain. 2. (of an ordering) constituting a total ordering. 3. (of a set of real numbers) having the property that if a and b are in the set and c lies between them, then c is also in the set, constituting a continuum. 4. (of a topological) set not able to be partitionedinto two non-empty open subsets each of which has no points in common with the closure of the other. For example, the rationals are not connected, although the reals are. The set is called path-, arc-, pathwise, or arcwise connected if each pair of points is joined by a path in the set; a connected set is not necessarily path-wise connected. 5. (of a graph) having the property that there is a path between every pair of vertices along a sequence of edges in the graph.