<abstract xmlns="http://www.w3.org/1999/xhtml">. 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 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.</abstract>

. 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 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.

Another proof of Hurewicz theorem

Mathematical Institute, Slovak Academy of Sciences, Jesenná 5, SK–041–54 Koˇsice, SLOVAKIA

Department of Computer Science, Faculty of Science, P. J. ˇSaf´arik University, Jesenn´a 5, SK-041-54 Koˇsice, SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"Another proof of Hurewicz theorem"}

. 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 Q̅ ∩ C = Q. We...

Another proof of Hurewicz theorem

Online veröffentlicht: 13. Nov. 2012

Seitenbereich: 1 - 7

DOI: https://doi.org/10.2478/v10127-011-0019-z

Schlüsselwörter
Hurewicz scheme, D-proper mapping, analytic set.

This content is open access.

Another proof of Hurewicz theorem

Online veröffentlicht: 13. Nov. 2012

Seitenbereich: 1 - 7

DOI: https://doi.org/10.2478/v10127-011-0019-z

SchlüsselwörterHurewicz scheme, D-proper mapping, analytic set.

This content is open access.

Schlüsselwörter
Hurewicz scheme, D-proper mapping, analytic set.