Disconnectivities are mathematical entities which stand in the way of a space being contractible (i.e., shrunk to a point, where the shrinking takes place inside the space itself). When dealing with topological spaces, a disconnectivity is interpreted as a "hole" in the space. Disconnectivities in space are studied through the extension problem or the lifting problem.

CITE THIS AS:

Weisstein, Eric W. "Disconnectivity." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Disconnectivity.html