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Extending Baire Property by countably many sets |
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| Authors: | Piotr Zakrzewski |
| Affiliation: | Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland |
| Abstract: | We prove that if ZFC is consistent so is ZFC + ``for any sequence  of subsets of a Polish space  there exists a separable metrizable topology  on  with  ,  and  Borel in  for all  .' This is a category analogue of a theorem of Carlson on the possibility of extending Lebesgue measure to any countable collection of sets. A uniform argument is presented, which gives a new proof of the latter as well. Some consequences of these extension properties are also studied. |
| Keywords: | Measure and category Borel sets Baire Property $sigma$-algebra $sigma$-ideal |
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