For $2$ manifolds $M,N$ with dimension $m>n$, the analytical injective function $i:N\rightarrow M$ is called analytical embedding and $i(N)$ is called Submanifold.
From the definition of manifolds a function must be a Homeomorphism in order to be a manifold which means the function musst be a bijection (along with some other criterias).
So I don't understand why an injective function can be a Submanifold?