Topological aspects of Hurewicz tests for the difference hierarchy
We generalize the Baire Category Theorem to the Borel and difference hierarchies, i.e. if Г is any of the classes Σξ⁰, Пξ⁰, Dη(Σξ⁰) or Ďη(Σξ⁰) we find a representative set Pг ∊ Г and a Polish topology τг such that for every A ∊ Ѓ from some assumption on the size of A ∩ Pг we can deduce that A\ Pг is...
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| Datum: | 2006 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2006
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| Schriftenreihe: | Український математичний вісник |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/124566 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Topological aspects of Hurewicz tests for the difference hierarchy / T. Matrai // Український математичний вісник. — 2006. — Т. 3, № 4. — С. 520-546. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We generalize the Baire Category Theorem to the Borel and difference hierarchies, i.e. if Г is any of the classes Σξ⁰, Пξ⁰, Dη(Σξ⁰) or Ďη(Σξ⁰) we find a representative set Pг ∊ Г and a Polish topology τг such that for every A ∊ Ѓ from some assumption on the size of A ∩ Pг we can deduce that A\ Pг is of second category in the topology τг. This allows us to distinguish the levels of the Borel and difference hierarchies via Baire category. We also present some typical Baire Category Theorem-like applications of the results. |
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