Kuratowski convergence
In mathematics, Kuratowski convergence is a notion of convergence for sequences (or, more generally, nets) of compact subsets of metric spaces, named after Kazimierz Kuratowski. Intuitively, the Kuratowski limit of a sequence of sets is where the sets "accumulate". Definitions. Let ("X", "d") be a metric space, where "X" is a set and "d" is the function of distance between points of "X". For any point "x" ∈ "X" and any non-empty compact subset "A" ⊆ "X", define the distance between the point and the subset: For any sequence of such subsets "A" ⊆ "X", "n" ∈  N, the Kuratowski limit inferior (or lower closed limit) of "A" as "n" → ∞ is the Kuratowski limit superior (or upper closed limit) of "A" as "n" → ∞ is If the Kuratowski limits inferior and superior agree (i.e. are the same subset of "X"), then their common value is called the Kuratowski limit of the sets "A" as "n" → ∞ and denoted Lt"A". The definitions for a general net of compact subsets of "X" go through "mutatis mutandis". Related Concepts. For metric spaces "X" we have the following: