Connected

From Exampleproblems

"Connected" is used in several senses:

• Two objects are connected if they are joined by some kind of connection.
• A person, building, city, organization, etc., is connected if it has or gives access to information technology.
• Connected is a 1992 album by the group Stereo MC's.
• In a number of fields of mathematics, an object is said to be connected if it is, in some sense, "all one piece". See connectedness for an overview of mathematical uses of this word. Articles specific to various fields of mathematics are listed below.
  • In topology, a connected space is a topological space that cannot be partitioned into two open sets.
  • In geometric topology, a connected sum of two connected m-dimensional manifolds is a manifold formed by deleting an open ball inside each manifold and gluing together the resulting boundary spheres.
  • In graph theory, a connected graph is a graph in which each pair of vertices is joined by a path.
  • In category theory, a connected category is a category in which, for each pair of objects A, B, there is at least one morphism from A to B.