Main Question or Discussion Point
In my book its says let i: U →M (but with a curved arrow) and calls it an inclusion map. What exactly is an inclusion map? Doesn't the curve arrow mean its 1-1? So are inclusion maps always 1-1?
Why would it be open?The curved arrow is usually reserved for inclusions. In general, if you have a differentiable manifold ##M## and a subset ##N \subseteq M## that is also a differentiable manifold then the inclusion map
$$\iota \colon N \to M \colon p \to p$$