In the textbook that I am currently reading, I faced a typo which I have specified in blue. The text goes as follows:
Assume that $W\subset\mathbb R^m$ and $V\subset\mathbb R^n$ are open sets, that $M$ is a subset of the product $\mathbb R^m \times \mathbb R^n=\mathbb R^{m+n},$ and $f:W\to V$ is a map whose graph is a subset of $M,$ i.e. $$\operatorname{graph}(f):=\{(x,y)\in W\times V|x\in W, y=f(x)\}\subset M.$$ Let $\color{blue} {U = (W \cap V)\cap \operatorname{graph}(f)}$ and let $\phi(x,y) = x$ be the projection of $U$ onto $W.$ Then the pair $(\phi,U)$ is a chart on $M.$
The blue part must be a typo, but I could not correct this as my correction would make this part a trivial expression. What is the correction?
(By definition, a chart on a set $M$ is a bijection from a subset of $M$ onto an open set in a Euclidean space.)