We obtain a criterion for approximability of piecewise linear maps S1 → R2 by embeddings, analogous to the one proved by Minc for piecewise linear maps I → R2. Theorem. Let φ : S1 → R2 be a piecewise linear map, which is simplicial for some triangulation of S1 with k vertices. The map φ is approximable by embeddings if and only if for each i = 0, . . . , k the i-th derivative φ(i) (defined by M...
