Use this tag for question on connected spaces and various related notions (connected components, locally connected spaces, pathwise/arcwise connected spaces, totally disconnected spaces ...) and for connectedness in graph theory.
A topological space is connected if it cannot be written as union of two disjoint non-empty open sets. Every topological space can be partitioned into connected components, which are connected subsets which are maximal with respect to inclusion.
Several related properties are studied in topology:
In graph theory, a connected graph is a graph such that there exists a path between any two vertices.