 Ultralimit

A point $x$ is the limit of a map $f:I\to X$ along an ultrafilter $\mathcal{U}$ on $I$ when $f^{-1}(V)\in \mathcal{U}$ for every neighbourhood $V$ of $x$. Every ultrafilter on a compact space has a limit, and that limit is unique in a Hausdorff space.

As of my last knowledge update in October 2023, "Ultralimit" could refer to various concepts depending on the context in which it is used. However, there wasn't a widely recognized or specific definition for "Ultralimit" in major fields such as technology, science, or popular culture.