Compactness for a topological space implies that every ultrafilter has this property.
Compactness for a topological space implies that every ultrafilter has this property. The Wisjman variety of this applies to closed subsets of metric spaces, the Gromov-Hausdorff metric helps define it for sequences of compact metric spaces, a property which is named for those men. In a complete metric space, a sequence being Cauchy (*) implies this property, and a test for it in series involves the ratio of a-sub-n over a-sub-n minus one being less than one. For 10 points, name this property which is possessed by a sequence that has a limit, indicating that its elements are approaching some finite value.
Compactness for a topological space implies that every ultrafilter has this property.
{convergence} [accept equivalents like “it {converges}” or “it has a {limit}”]