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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| Published in: | Український математичний вісник |
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| Date: | 2006 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/124566 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862721913730629632 |
|---|---|
| author | Matrai, T. |
| author_facet | Matrai, T. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | 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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| first_indexed | 2025-12-07T18:33:25Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-124566 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T18:33:25Z |
| publishDate | 2006 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Matrai, T. 2017-09-29T10:51:06Z 2017-09-29T10:51:06Z 2006 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. 1810-3200 2000 MSC. 03E15, 54H05, 28A05. https://nasplib.isofts.kiev.ua/handle/123456789/124566 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. en Інститут прикладної математики і механіки НАН України Український математичний вісник Topological aspects of Hurewicz tests for the difference hierarchy Article published earlier |
| spellingShingle | Topological aspects of Hurewicz tests for the difference hierarchy Matrai, T. |
| title | Topological aspects of Hurewicz tests for the difference hierarchy |
| title_full | Topological aspects of Hurewicz tests for the difference hierarchy |
| title_fullStr | Topological aspects of Hurewicz tests for the difference hierarchy |
| title_full_unstemmed | Topological aspects of Hurewicz tests for the difference hierarchy |
| title_short | Topological aspects of Hurewicz tests for the difference hierarchy |
| title_sort | topological aspects of hurewicz tests for the difference hierarchy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/124566 |
| work_keys_str_mv | AT matrait topologicalaspectsofhurewicztestsforthedifferencehierarchy |