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>.

Solution

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

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An immersed submanifold of $M$ is a manifold $N$ with an injective immersion $\iota:N\to M$; when $N$ is treated as a subset, its manifold topology can be finer than its subspace topology.


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