# Is a minimal Hausdorff uniformity compact?

Let $(X,\mathcal D)$ be a Hausdorff uniform space and for each Hausdorff uniformity $\mathcal U$ on $X$, $$\mathcal U \subseteq\mathcal D\to \mathcal U =\mathcal D$$

Is $(X,\mathcal D)$ compact?

The following are equivalent for a Tychonov space $X$:
1. $X$ is locally compact.
2. There is a minimal uniformity on $X$.