---
tag: 3R9GQGFHP5
kind: concept
name: Ultralimit
aliases: [asymptotic-cone]
sources:
  - wikipedia: en:18609360@r1362178993
    locator: Ultralimit
    note: adopted
    mention: wikipedia://en/18609360
    sections: [Summary]
same_as:
  wikidata: Q3548074
  wikipedia: Ultralimit
inventory: [6HKN2MRM6Y]
---

## Summary

In mathematics, an **ultralimit** is a geometric construction that assigns a limit [[metric space|063W5JMY85]] to a sequence of metric spaces $X_n$. The concept captures the limiting behavior of finite configurations in the $X_n$ spaces employing an ultrafilter to bypass the need for repeated consideration of subsequences to ensure convergence. Ultralimits generalize Gromov–Hausdorff convergence in metric spaces.