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...
Saved in:
| Date: | 2006 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2006
|
| Series: | Український математичний вісник |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/124566 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
|---|