- Tytuł:
- An abstract version of Sierpińskis theorem and the algebra generated by A and CA functions
- Autorzy:
-
Cichoń, J.
Morayne, Michał - Powiązania:
- https://bibliotekanauki.pl/articles/1208631.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
analytic sets
universal functions
Baire function
uniform closure
cardinal number - Opis:
- We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass of the space of all functions measurable with respect to the least class containing intersections of analytic and coanalytic sets and which is closed under countable unions (A and CA functions are analogues of lower and upper semicontinuous functions, respectively, when measurability with respect to open sets is replaced by that with respect to analytic sets).
- Źródło:
-
Fundamenta Mathematicae; 1993, 142, 3; 263-268
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł