Submanifolds with codimension $0$

Question

So pretty much as the title said, I'm supposed to find all submanifolds of $\mathbb{R}^n$ with codimension $0$.

I haven't got too far but here are some of my thoughts:

1. I started with intuitive thinking. If the submanifold were of the dimension $k<n$, then the mapping would need to provide us an open set that looks like a "flattened out version of the submanifold intersected with a neighborhood". But in this case, our mapping "doesn't do anything special". To me, it just seems as a "translation of a set" in $\mathbb{R}^n$.
2. If I got it right, the trivial case would be $\mathbb{R}^n$ as a submanifold of itself.
3. Since the function $\varphi:T \rightarrow M \cap U$ is an immersion (so $\varphi ^ \prime \neq 0$), inverse function theorem can be applied, but other than getting a local diffeomorphism, I'm not sure if it's of any help.

For further context, I would like to mention that we did not define manifolds, only submanifolds.

Any hint would be appreciated. Thanks in advance!

Edit: for anyone reading this in the future, refer to the linked post, there's the answer to my question.