Autor: Morayne, Michał - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

Skocz do pozycji: 2.

Tytuł:: Algebras of Borel measurable functions
Autorzy:: Morayne, Michał
Powiązania:: https://bibliotekanauki.pl/articles/1214950.pdf
Data publikacji:: 1992
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Źródło:: Fundamenta Mathematicae; 1992, 141, 3; 229-242
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Measure preserving analytic diffeomorphisms of countable dense sets in $C^n$ and $R^n$
Autorzy:: Morayne, Michał
Powiązania:: https://bibliotekanauki.pl/articles/724768.pdf
Data publikacji:: 1987
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Źródło:: Colloquium Mathematicum; 1987, 52, 1; 93-98
0010-1354
Pojawia się w:: Colloquium Mathematicum
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Artykuł

Skocz do pozycji: 5.

Artykuł

Skocz do pozycji: 6.

Tytuł:: Sierpińskis hierarchy and locally Lipschitz functions
Autorzy:: Morayne, Michał
Powiązania:: https://bibliotekanauki.pl/articles/1208370.pdf
Data publikacji:: 1995
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: Let Z be an uncountable Polish space. It is a classical result that if I ⊆ ℝ is any interval (proper or not), f: I → ℝ and $α < ω_1$ then f ○ g ∈ $B_α(Z)$ for every $g ∈ B_α(Z) ∩^ZI$ if and only if f is continuous on I, where $B_α(Z)$ stands for the αth class in Baire's classification of Borel measurable functions. We shall prove that for the classes $S_α(Z) (α > 0)$ in Sierpiński's classification of Borel measurable functions the analogous result holds where the condition that f is continuous is replaced by the condition that f is locally Lipschitz on I (thus it holds for the class of differences of semicontinuous functions, which is the class $S_1(Z)$). This theorem solves the problem raised by the work of Lindenbaum ([L] and [L, Corr.]) concerning the class of functions not leading outside $S_α(Z)$ by outer superpositions.
Źródło:: Fundamenta Mathematicae; 1995, 147, 1; 73-82
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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