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connectivity number

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connectivity number [kə‚nek′tiv·əd·ē ‚nəm·bər]
(mathematics)
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, then-dimensional connectivity number of a topological spaceXis the number of infinite cyclic groups whose direct sum with the torsion groupGn(X) forms the homology groupHn(X).


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