On the Class of Perfectly Null Sets and Its Transitive Version

• Autorzy: Korch M. , Weiss T.

Identyfikatory

DOI

10.4064/ba8029-5-2016

• Języki publikacji: EN

Abstrakty

EN

We introduce two new classes of special subsets of the real line: the class of perfectly null sets and the class of sets which are perfectly null in the transitive sense. These classes may play the role of duals to the corresponding classes on the category side. We investigate their properties and, in particular, we prove that every strongly null set is perfectly null in the transitive sense, and that it is consistent with ZFC that there exists a universally null set which is not perfectly null in the transitive sense. Finally, we state some open questions concerning the above classes. Although the main problem of whether the classes of perfectly null sets and universally null sets are consistently different remains open, we prove some results related to this question.

Słowa kluczowe

EN

perfectly null sets; sets perfectly null in the transitive sense; special subsets of the real line; Cantor space

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2016
• Tom: Vol. 64, no. 1
• Strony: 1--20
• Opis fizyczny: Bibliogr. 24 poz., rys., tab.

Twórcy

autor

Korch M.

• Institute of Mathematics, University of Warsaw, 02-097 Warszawa, Poland

autor

Weiss T.

• Institute of Mathematics, Cardinal Stefan Wyszyński University in Warsaw, 01-938 Warszawa, Poland

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.