How can we construct *Fine uniformities*?

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Given a uniformizable (w.r.t. entourage uniformity) space $X$ there is a finest uniformity on $X$ compatible with the topology of $X$ called the fine uniformity or universal uniformity. A uniform space is said to be fine if it has the fine uniformity generated by its uniform topology.

why the fine uniformity is exists and How we can construct it? the completely regularity is needed to construct the fine uniformity?

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why the fine uniformity exists

It is supremum of all compatible uniformities on $X$.

and How we can construct it?

I guess its base should be a family of all open entourages of the diagonal $U$ such that there exists a sequence $\{U_n\}$ of open entourages such that $U_0=U$ and $U_{n+1}^2\subset U_n$ for each $n$.

the completely regularity is needed to construct the fine uniformity?

Yes, a topological space is uniformizable space iff it is completely regular.