Geodesic
Some properties of the spaces $T(k,\tau)$ and $S(k,\tau)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 209-221
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The properties of two families of $h$-homogeneous Borel sets $\{T(k,\tau)\colon\omega\leq\tau\leq k\}$ and $\{S(k,\tau)\colon\omega\leq\tau\leq k\}$ are studied. The sets of the former family are obtained as the result of taking the union of the Baire space $B(k)$ and the $\sigma$-discrete space $Q(k)$, while the sets of the latter family are obtained as the result of taking the union of the spaces $B(k)$ and $Q(k)\times C$. We prove theorems on the embedding of these sets into absolute Souslin sets as closed subsets.
Keywords: $h$-homogeneous space, Souslin set, $\sigma LW({<}k)$-space, embedding, homeomorphism.
Mots-clés : Baire space 
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S. V. Medvedev. Some properties of the spaces $T(k,\tau)$ and $S(k,\tau)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 209-221. http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a21/

[1] Stone A. H., “Non-separable Borel sets”, Rozpr. Mat., 28 (1962), 1–40 | MR

[2] Stone A. H., “Non-separable Borel sets, II”, Gen. Topol. Appl., 2 (1972), 249–270 | DOI | MR | Zbl

[3] Medvedev S. V., “Topologicheskie kharakteristiki prostranstv $Q(k)$ i $Q\times B(k)$”, Vestn. Mosk. un-ta. Ser. 1. Matematika. Mekhanika, 1986, no. 1, 47–49 | MR | Zbl

[4] Medvedev S. V., “Nulmernye odnorodnye borelevskie mnozhestva”, Dokl. AN SSSR, 283:3 (1985), 542–545 | MR | Zbl

[5] Medvedev S. V., “Vlozhenie proizvedenii $Q(k)\times C$ i $Q(k)\times B(\omega)$ v absolyutnye $A$-mnozhestva”, Izv. Chelyab. nauch. tsentra, 4(46) (2009), 7–12 | MR

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

[7] Medvedev S. V., “O svyazi mezhdu $h$-odnorodnymi prostranstvami pervoi i vtoroi kategorii”, Otobrazheniya i rasshireniya topologicheskikh prostranstv, sb. nauchn. tr., Udmurt. gos. un-t, Ustinov, 1985, 33–42

[8] Medvedev S. V., “O vlozhenii berovskogo prostranstva $B(k)$ v absolyutnye $A$-mnozhestva”, Vestn. Yuzhno-Ural. gos. un-ta. Matematika, fizika, khimiya, 10(143):12 (2009), 27–32

[9] Engelking R., Obschaya topologiya, Mir, M., 1986, 752 pp. | MR

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

[11] Medvedev S. V., “K voprosu o prostranstvakh pervoi kategorii”, Vestn. Mosk. un-ta. Ser. 1. Matematika. Mekhanika, 1986, no. 2, 84–86 | MR | Zbl