Ultralimit
- For the direct limit of a sequence of ultrapowers, see Ultraproduct.
In mathematics, an ultralimit is a geometric construction that assigns to a sequence of metric spaces Xn a limiting metric space. The notion of an ultralimit captures the limiting behavior of finite configurations in the spaces Xn and uses an ultrafilter to avoid the process of repeatedly passing to subsequences to ensure convergence. An ultralimit is a generalization of the notion of Gromov-Hausdorff convergence of metric spaces.