On universality of countable powers of absolute retracts
We construct an absolute retract X of arbitrarily high Borel complexity such that the countable power X ω is not universal for the Borelian class A 1 of sigma-compact spaces, and the product X ω x ∑, where ∑ is the radial interior of the Hilbert cube, is not universal for the Borelian class A 2 of a...
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| Date: | 1996 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5317 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511537064574976 |
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| author | Banakh, T. O. Radyl, Т. Банах, Т. О. Раділ, Т. |
| author_facet | Banakh, T. O. Radyl, Т. Банах, Т. О. Раділ, Т. |
| author_sort | Banakh, T. O. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:30:10Z |
| description | We construct an absolute retract X of arbitrarily high Borel complexity such that the countable power X ω is not universal for the Borelian class A 1 of sigma-compact spaces, and the product X ω x ∑, where ∑ is the radial interior of the Hilbert cube, is not universal for the Borelian class A 2 of absolute G δσ-spaces. |
| first_indexed | 2026-03-24T03:14:28Z |
| format | Article |
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| id | umjimathkievua-article-5317 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:14:28Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/c5/2efafe0e87c332972693485160301ac5.pdf |
| spelling | umjimathkievua-article-53172020-03-18T21:30:10Z On universality of countable powers of absolute retracts On universality of countable powers of absolute retracts Banakh, T. O. Radyl, Т. Банах, Т. О. Раділ, Т. We construct an absolute retract X of arbitrarily high Borel complexity such that the countable power X ω is not universal for the Borelian class A 1 of sigma-compact spaces, and the product X ω x ∑, where ∑ is the radial interior of the Hilbert cube, is not universal for the Borelian class A 2 of absolute G δσ-spaces. Побудовано абсолютний ретракт $X$ як завгодно високої борелівської складності, зліченна степінь якого $X^{ω}$ не універсальна для борелівського класу $A_1$ що складається з сігма-компактних просторів. Доведено, що добуток $X^{ω} \times ∑$ не є універсальним для борелівського класу $A_2$ абсолютних $G_{δσ}$-просторів (тут $∑$ - радіальна внутрішність гільбергового куба). Institute of Mathematics, NAS of Ukraine 1996-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5317 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 4 (1996); 540-542 Український математичний журнал; Том 48 № 4 (1996); 540-542 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/5317/7325 https://umj.imath.kiev.ua/index.php/umj/article/view/5317/7326 Copyright (c) 1996 Banakh T. O.; Radyl Т. |
| spellingShingle | Banakh, T. O. Radyl, Т. Банах, Т. О. Раділ, Т. On universality of countable powers of absolute retracts |
| title | On universality of countable powers of absolute retracts |
| title_alt | On universality of countable powers of absolute retracts |
| title_full | On universality of countable powers of absolute retracts |
| title_fullStr | On universality of countable powers of absolute retracts |
| title_full_unstemmed | On universality of countable powers of absolute retracts |
| title_short | On universality of countable powers of absolute retracts |
| title_sort | on universality of countable powers of absolute retracts |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5317 |
| work_keys_str_mv | AT banakhto onuniversalityofcountablepowersofabsoluteretracts AT radylt onuniversalityofcountablepowersofabsoluteretracts AT banahto onuniversalityofcountablepowersofabsoluteretracts AT radílt onuniversalityofcountablepowersofabsoluteretracts |