Some properties of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">I</mml:mi></mml:math>-Luzin sets

Michalski, Marcin; Żeberski, Szymon

doi:10.1016/j.topol.2015.04.007

Cited by 5 publications

(6 citation statements)

References 11 publications

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“…Before we proceed to the main theorem of this section let us recall a generalized version of Rothberger's theorem (see [13]). The following theorem extends the result obtained in [9].…”

Section: Let Us Approximate λ([Tsupporting

confidence: 86%

Nonmeasurable sets and unions with respect to tree ideals

Michalski,

Rałowski,

Żeberski

2017

Preprint

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In this paper we consider a notion of nonmeasurablity with respect to Marczewski and Marczewski-like tree ideals s 0 , m 0 , l 0 , and cl 0 . We show that there exists a subset A of the Baire space ω ω which is s-, l-, and m-nonmeasurable, that forms dominating m.e.d. family. We introduce and investigate a notion of T-Bernstein setssets that intersect but does not containt any body of a tree from a given family of trees T. We also acquire some results on I-Luzin sets, namely we prove that there are no m 0 -, l 0 -, and cl 0 -Luzin sets and that if c is a regular cardinal, then the algebraic sum (considered on the real line R) of a generalized Luzin set and a generalized Sierpiński set belongs to s 0 , m 0 , l 0 and cl 0 .Definition 1. Let T be a tree on a set A. Then

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“…Before we proceed to the main theorem of this section let us recall a generalized version of Rothberger's theorem (see [13]). The following theorem extends the result obtained in [9].…”

Section: Let Us Approximate λ([Tsupporting

confidence: 86%

Nonmeasurable sets and unions with respect to tree ideals

Michalski,

Rałowski,

Żeberski

2017

Preprint

Self Cite

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“…Proof. Let P ⊆ R be a perfect set such that P ∩ (P + x) is at most 1-point for x = 0 (see [5]). Let us set B = {(x, y) :…”

Section: Preserving Smital Properties Via Productsmentioning

confidence: 99%

Ideals with Smital properties

Michalski¹,

Rałowski²,

Żeberski³

2021

Preprint

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“…The notion of complete Laver trees was defined and investigated in [7], although Miller in [6] defines Laver trees de facto as complete Laver trees and Hechler trees as complete Hechler trees.…”

Section: Definition 2 a Tree T On Is Called Amentioning

confidence: 99%

“…I-Luzin sets and algebraic properties. Let us recall the notion of I-Luzin sets (see [6]). Let X be a Polish space and I be an ideal.…”

Section: Definition 2 a Tree T On Is Called Amentioning

confidence: 99%

Nonmeasurable Sets and Unions With Respect to Tree Ideals

Michalski¹,

Rałowski²,

Żeberski³

2020

Bull. symb. log

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In this paper, we consider a notion of nonmeasurablity with respect to Marczewski and Marczewski-like tree ideals s 0 , m 0 , l 0 , cl 0 , h 0 , and ch 0. We show that there exists a subset of the Baire space , which is s-, land nd m-nonmeasurable that forms a dominating m.e.d. family. We investigate a notion of T-Bernstein sets-sets which intersect but do not contain any body of any tree from a given family of trees T. We also obtain a result on I-Luzin sets, namely, we prove that if c is a regular cardinal, then the algebraic sum (considered on the real line R) of a generalized Luzin set and a generalized Sierpiński set belongs to s 0 , m 0 , l 0 , and cl 0 .

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Some properties ofI-Luzin sets

Cited by 5 publications

References 11 publications

Nonmeasurable sets and unions with respect to tree ideals

Nonmeasurable sets and unions with respect to tree ideals

Ideals with Smital properties

Nonmeasurable Sets and Unions With Respect to Tree Ideals

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