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High Quality Content by WIKIPEDIA articles! In mathematics, Kuratowski convergence is a notion of convergence for sequences (or, more generally, nets) of compact subsets of metric spaces, named after the Polish mathematician Kazimierz Kuratowski. Intuitively, the Kuratowski limit of a sequence of sets is where the sets accumulate . In mathematics, more specifically general topology and metric topology, a compact space is an abstract mathematical space in which, intuitively, whenever one takes an infinite number of steps in the space, eventually one must get arbitrarily close to some other point of the space. Thus a closed and bounded subset (such as a closed interval or rectangle) of a Euclidean space is compact because ultimately one's steps are forced to bunch up near a point of the set, a result known as the Bolzano-Weierstrass theorem, whereas Euclidean space itself is not compact because one can take infinitely many equal steps in any given direction without ever getting very close to any other point of the spacee.

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