Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 115 / 2 / a / Solution

An immersed submanifold of $M$ is a manifold $N$ with an injective immersion $\iota :N\to M$. It is an embedded submanifold when $\iota$ is also a homeomorphism onto its image with the subspace topology, equivalently when it is a smooth embedding.