Add a couple of clarifications that U(p) is an open neighborhood

src/ga/05topology_inv.tex

@@ -157,7 +157,7 @@ \subsection{Compactness and paracompactness}
 Any subcover of a cover is a refinement of that cover, but the converse is not true in general. A refinement $R$ is said to be:
 \bit
 \item \emph{open} if $R\se \cO$;
-\item \emph{locally finite} if for any $p\in M$ there exists a neighbourhood $U(p)$ such that the set:
+\item \emph{locally finite} if for any $p\in M$ there exists an open neighbourhood $U(p)$ such that the set:
 \bse
 \{U \in R \mid U \cap U(p) \neq \vn\}
 \ese
@@ -201,7 +201,7 @@ \subsection{Compactness and paracompactness}
 \bd
 Let $(M,\cO_M)$ be a topological space. A \emph{partition of unity}\index{partition of unity}  of $M$ is a set $\cF$ of continuous maps from $M$ to the interval $[0,1]$ such that for each $p\in M$ the following conditions hold:
 \ben
-\item[i)] there exists $U(p)$ such that the set $\{f \in \cF \mid \forall \, x \in U(p):f(x)\neq 0\}$ is finite;
+\item[i)] there exists an open neighbourhood $U(p)$ such that the set $\{f \in \cF \mid \forall \, x \in U(p):f(x)\neq 0\}$ is finite;
 \item[ii)] $\sum_{f\in \cF}f(p)=1$.
 \een
 If $C$ is an open cover, then $\cF$ is said to be \emph{subordinate} to the cover $C$ if: