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