# Another proof of Hurewicz theorem

In: Tatra Mountains Mathematical Publications, vol. 49, no. 2
Miroslav Repický

## Details:

Year, pages: 2011, 1 - 7
Keywords:
Hurewicz scheme, $D$-proper mapping, analytic set
A Hurewicz theorem says that every coanalytic non-$Gδ$ 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 $κ$-Suslin sets. As a consequence, under Martin's Axiom, we obtain a characterization of $\boldsymbolΣ12$ sets that are the unions of less than the continuum closed sets.