A semifilter approach to selection principles

Lubomyr Zdomsky

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 3, page 525-539
  • ISSN: 0010-2628

Abstract

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In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal 𝔤 is a lower bound of the additivity number of the σ -ideal generated by Menger subspaces of the Baire space, and under 𝔲 < 𝔤 every subset X of the real line with the property Split ( Λ , Λ ) is Hurewicz, and thus it is consistent with ZFC that the property Split ( Λ , Λ ) is preserved by unions of less than 𝔟 subsets of the real line.

How to cite

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Zdomsky, Lubomyr. "A semifilter approach to selection principles." Commentationes Mathematicae Universitatis Carolinae 46.3 (2005): 525-539. <http://eudml.org/doc/249532>.

@article{Zdomsky2005,
abstract = {In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal $\mathfrak \{g\}$ is a lower bound of the additivity number of the $\sigma $-ideal generated by Menger subspaces of the Baire space, and under $\mathfrak \{u\} < \mathfrak \{g\}$ every subset $X$ of the real line with the property $\operatorname\{Split\} (\Lambda ,\Lambda )$ is Hurewicz, and thus it is consistent with ZFC that the property $\operatorname\{Split\} (\Lambda ,\Lambda )$ is preserved by unions of less than $\mathfrak \{b\}$ subsets of the real line.},
author = {Zdomsky, Lubomyr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Menger property; Hurewicz property; property $\operatorname\{Split\}(\Lambda , \Lambda )$; semifilter; multifunction; small cardinals; additivity number; Menger property; Hurewicz property},
language = {eng},
number = {3},
pages = {525-539},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A semifilter approach to selection principles},
url = {http://eudml.org/doc/249532},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Zdomsky, Lubomyr
TI - A semifilter approach to selection principles
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 3
SP - 525
EP - 539
AB - In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal $\mathfrak {g}$ is a lower bound of the additivity number of the $\sigma $-ideal generated by Menger subspaces of the Baire space, and under $\mathfrak {u} < \mathfrak {g}$ every subset $X$ of the real line with the property $\operatorname{Split} (\Lambda ,\Lambda )$ is Hurewicz, and thus it is consistent with ZFC that the property $\operatorname{Split} (\Lambda ,\Lambda )$ is preserved by unions of less than $\mathfrak {b}$ subsets of the real line.
LA - eng
KW - Menger property; Hurewicz property; property $\operatorname{Split}(\Lambda , \Lambda )$; semifilter; multifunction; small cardinals; additivity number; Menger property; Hurewicz property
UR - http://eudml.org/doc/249532
ER -

References

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