connectivity number[kə‚nek′tiv·əd·ē ‚nəm·bər]
The number of points plus 1 which can be removed from a curve without separating the curve into more than one piece.
The number of closed cuts or cuts joining points of previous cuts (or joining points on the boundary) plus 1 which can be made on a surface without separating the surface. Also known as Betti number.
In general, the n-dimensional connectivity number of a topological space X is the number of infinite cyclic groups whose direct sum with the torsion group Gn (X) forms the homology group Hn (X).