Reorganised the completion of uniform spaces.

src/topology/uniform/completion.tex

@@ -8,7 +8,7 @@
     \begin{enumerate}
         \item $(\wh X, \wh \fU)$ is a complete Hausdorff uniform space.
         \item $\iota \in UC(X; \wh X)$.
-        \item[(U)] For any pair $(Y, f)$ satisfying (1) and (2), there exists unique $F \in C(\wh X; Y)$ such that the following diagram commutes
+        \item[(U)] For any complete Hausdorff uniform space $Y$ and Cauchy continuous function $f: X \to Y$, there exists unique $F \in C(\wh X; Y)$ such that the following diagram commutes
 
         \[
         \xymatrix{
@@ -17,7 +17,7 @@
         }
         \]
 
-        and $F \in UC(\wh X; Y)$.
+        Moreover, if $f \in UC(X; Y)$, then $F \in UC(\wh X; Y)$.
     \end{enumerate}
     Moreover,
     \begin{enumerate}