Update 1-manifolds.tex

1-manifolds.tex

@@ -574,7 +574,7 @@ \section{Smooth maps and differentiability}\label{sec:smoothfn}
 	\caption{A function is differentiable if it is differentiable as a euclidean function through the magnifying lens provided by the charts.}
 \end{marginfigure}
 \begin{definition}
-	A function $f:M\to\R$ from a smooth manifold $M$ of dimension $n$ to $\R$ is \emph{smooth}, or \emph{of class $C^\infty$}, if for any smooth chart $(\varphi, V)$ for $M$ the map $f\circ\varphi^{-1}:\varphi(V)\subset\R^n \to \R$ is smooth as a euclidean function on the open subset $\varphi(V)\subset\R^n$.
+	A function $f:M\to\R$ from a smooth manifold $M$ of dimension $n$ to $\R$ is \emph{smooth}, or \emph{of class $C^\infty$}, if for any smooth chart $(V, \varphi)$ for $M$ the map $f\circ\varphi^{-1}:\varphi(V)\subset\R^n \to \R$ is smooth as a euclidean function on the open subset $\varphi(V)\subset\R^n$.
 	We denote the space of smooth functions by $C^\infty(M)$.
 \end{definition}