ANOTHER PROOF OF HUREWICZ THEOREM

Abstract

A~Hurewicz theorem says that every coanalytic non-$G_\delta$~set~$C$
in a~Polish space contains a~countable set~$Q$ without isolated points
such that $\overline Q\cap C=Q$.
We present another elementary proof of this theorem and generalize it
for $\kappa$-Suslin sets.
As a~consequence, under Martin's Axiom, we obtain a~characterization
of $\boldsymbol\Sigma^1_2$~sets that are the unions of less
than the continuum closed sets.