Another proof of Hurewicz theorem

. A Hurewicz theorem says that every coanalytic non-G_δ set C in a Polish space contains a countable set Q without isolated points such that Q̅ ∩ C = Q. We present another elementary proof of this theorem and generalize it for k-Suslin sets. As a consequence, under Martin’s Axiom, we obtain a characterization of ∑¹₂ sets that are the unions of less than the continuum closed sets.