I'm reading through Lee's Introduction to Smooth Manifolds and wondered why local submersions or local immersions are not studied.
Let $M$ and $N$ be smooth manifolds (with or without boundary) and let $F:M\to N$ be a smooth map between them.
Definition: if any point $p\in M$ has a neighborhood $U$ such that $F(U)$ is open and $F|_U$ is a diffeomorphism, submersion, or immersion, then we call $F$ a local diffeomorphism, local submersion, or local immersion, respectively.
Local diffeomorphisms are properly studied in the book, but local submersions and local immersions are not present. Why is this so?