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Ultralimit

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In mathematics, an ultralimit is a geometric construction that assigns a limit metric space to a sequence of metric spaces X n {\displaystyle X_{n}} . The concept captures the limiting behavior of finite configurations in the X n {\displaystyle X_{n}} spaces employing an ultrafilter to bypass the need for repeated consideration of subsequences to ensure convergence. Ultralimits generalize Gromov–Hausdorff convergence in metric spaces.