Update 1-manifolds.tex

1-manifolds.tex

@@ -979,7 +979,7 @@ \section{Manifolds with boundary}\label{sec:mbnd}
 	\marginnote{The boundary $\partial M$ as defined by~\eqref{def:bdry} can differ from its topological boundary as a subset of another topological space. For example the boundary $\partial\bS^1$ of the circle as a manifold is empty, but the boundary of the circle $\bS^1$ as a subset of $\R^2$ is $\bS^1$ itself.}
 	The \emph{boundary} of $M$ is defined as
 	\begin{equation}\label{def:bdry}
-		\partial M := \bigcup_{\alpha\in A} \varphi_\alpha^{-1}\left(\varphi_\alpha(V_\alpha)\cap \partial\cH^n\right).
+		\partial M := \bigcup_{\alpha\in A} \varphi_\alpha^{-1}\left(\varphi_\alpha(U_\alpha)\cap \partial\cH^n\right).
 	\end{equation}
 \end{definition}