Geodesic
A semifilter approach to selection principles
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 525-539

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR   Zbl

In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal $\frak g$ is a lower bound of the additivity number of the $\sigma$-ideal generated by Menger subspaces of the Baire space, and under $\frak u \frak g$ 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 $\frak b$ subsets of the real line.
In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal $\frak g$ is a lower bound of the additivity number of the $\sigma$-ideal generated by Menger subspaces of the Baire space, and under $\frak u \frak g$ 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 $\frak b$ subsets of the real line.
Classification : 03Axx, 03E17, 03E35, 54D20
Keywords: Menger property; Hurewicz property; property $\operatorname{Split}(\Lambda, \Lambda )$; semifilter; multifunction; small cardinals; additivity number 
Zdomsky, Lubomyr. A semifilter approach to selection principles. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 525-539. http://geodesic.mathdoc.fr/item/CMUC_2005_46_3_a13/
@article{CMUC_2005_46_3_a13,
     author = {Zdomsky, Lubomyr},
     title = {A semifilter approach to selection principles},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {525--539},
     year = {2005},
     volume = {46},
     number = {3},
     mrnumber = {2174530},
     zbl = {1121.03060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2005_46_3_a13/}
}
TY  - JOUR
AU  - Zdomsky, Lubomyr
TI  - A semifilter approach to selection principles
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2005
SP  - 525
EP  - 539
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMUC_2005_46_3_a13/
LA  - en
ID  - CMUC_2005_46_3_a13
ER  - 
%0 Journal Article
%A Zdomsky, Lubomyr
%T A semifilter approach to selection principles
%J Commentationes Mathematicae Universitatis Carolinae
%D 2005
%P 525-539
%V 46
%N 3
%U http://geodesic.mathdoc.fr/item/CMUC_2005_46_3_a13/
%G en
%F CMUC_2005_46_3_a13