Kuratowski's intersection theorem

In mathematics, Kuratowski's intersection theorem is a result in general topology that gives a sufficient condition for a nested sequence of sets to have a non-empty intersection. Kuratowski's result is a generalisation of Cantor's intersection theorem. Whereas Cantor's result requires that the sets involved be compact, Kuratowski's result allows them to be non-compact, but insists that their non-compactness "tends to zero" in an appropriate sense. The theorem is named for the Polish mathematician Kazimierz Kuratowski, who proved it in 1930.