Q: Torus in a torus Let $\mathbb{T}^n$ be a n-dimensional torus and $M\subseteq \mathbb{T}^n$ be a submanifold homoemorphic to $\mathbb{T}^n$. Do we have necessarily have $M=\mathbb{T}^n$?

A: Yes, since the dimension of $M$ is $n$, $M$ is open in $\mathbb{T}^n$, it is also closed since it is compact, since $\mathbb{T}^n$ is connected, $M=\mathbb{T}^n$.
