Actually atAt first I thought that if a subspace of R^n$\mathbb{R}^n$ is homeomorphic to a manifold,
is then it is a C^0submanifold$C^0$ submanifold of R^n$\mathbb{R}^n$. But I found an asterisked exercise in the book Differential TopologyDifferential Topology by Morris Hirsch that was "ifsaid ``if a subset of R^2$\mathbb{R}^2$ is homeomorphic to S^1$S^1$ then it is a C^0$C^0$ submanifold of R^2"$\mathbb{R}^2$'' which requires Schoenflies' Theorem to prove (given as a hint). As this special case requires that much machineriesmachinery, I think in general it is not true. Kindly provide an answer.
