Geodesic
Embedding of Products $Q(k)\times B(\tau)$ in Absolute $A$-Sets
Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 408-421.

Voir la notice de l'article provenant de la source Math-Net.Ru

Theorems about closed embeddings in absolute $A$-sets of the products $Q(k)\times B(\tau)$, $Q(k)\times \nobreak\mathscr N$, and $Q(k)\times C$ are proved. These are generalizations to the nonseparable case of theorems of Saint-Raymond, van Mill, and van Engelen about closed embeddings in separable absolute Borel sets of the products $Q\times \mathscr N$ and $Q\times C$, where $Q$ is the space of rational numbers, $C$ is the Cantor perfect set, and $\mathscr N$ is the space of irrational numbers.
Keywords: rational and irrational numbers, Cantor set, absolute $A$-set, $G_\delta$-set, $F_\sigma$-set, closed embedding, metric space, complete metric space, absolute Borel set
Mots-clés : Baire space. 
@article{MZM_2011_90_3_a6,
     author = {S. V. Medvedev},
     title = {Embedding of {Products} $Q(k)\times B(\tau)$ in {Absolute} $A${-Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {408--421},
     publisher = {mathdoc},
     volume = {90},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a6/}
}
TY  - JOUR
AU  - S. V. Medvedev
TI  - Embedding of Products $Q(k)\times B(\tau)$ in Absolute $A$-Sets
JO  - Matematičeskie zametki
PY  - 2011
SP  - 408
EP  - 421
VL  - 90
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a6/
LA  - ru
ID  - MZM_2011_90_3_a6
ER  - 
%0 Journal Article
%A S. V. Medvedev
%T Embedding of Products $Q(k)\times B(\tau)$ in Absolute $A$-Sets
%J Matematičeskie zametki
%D 2011
%P 408-421
%V 90
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a6/
%G ru
%F MZM_2011_90_3_a6
S. V. Medvedev. Embedding of Products $Q(k)\times B(\tau)$ in Absolute $A$-Sets. Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 408-421. http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a6/

[1] J. Saint-Raymond, “La structure borélienne d'Effros est-elle standard?”, Fund. math., 100:3 (1978), 201–210 | MR | Zbl

[2] F. van Engelen, J. van Mill, “Borel sets in compact spaces: some Hurewicz type theorems”, Fund. Math., 124:3 (1984), 271–286 | MR | Zbl

[3] A. H. Stone, “Non-separable Borel sets”, Rozpr. Mat., 28 (1962) | MR | Zbl

[4] A. H. Stone, “Non-separable Borel sets, II”, General Topology and Appl., 2:3 (1972), 249–270 | DOI | MR | Zbl

[5] S. V. Medvedev, “Neseparabelnye $h$-odnorodnye metricheskie prostranstva”, Kardinalnye invarianty i otobrazheniya topologicheskikh prostranstv, Udmurtskii gos. un-t, Izhevsk, 1984, 58–63 | MR

[6] S. V. Medvedev, Obobschenie dvukh teorem Gurevicha na neseparabelnyi sluchai, Dep. v VINITI No 6823-84

[7] R. Engelking, Obschaya topologiya, Mir, M., 1986 | MR | Zbl

[8] R. W. Hansell, “On characterizing non-separable analytic and extended Borel sets as types of continuous images”, Proc. London Math. Soc. (3), 28:4 (1974), 683–699 | DOI | MR | Zbl

[9] S. V. Medvedev, “Prodolzhenie gomeomorfizmov v nulmernykh metricheskikh prostranstvakh”, Voprosy geometrii i topologii, Petrozavodskii gos. un-t, Petrozavodsk, 1986, 41–50 | MR