Geodesic
Some topological properties of $\omega$-covering sets
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 865-877 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We prove the following theorems: There exists an ${\omega }$-covering with the property $s_0$. Under $\mathop {\mathrm cov}\nolimits ({\mathcal N}) = $ there exists $X$ such that $ \forall _{B \in {\mathcal B}or} [B\cap X$ is not an ${\omega }$-covering or $X\setminus B$ is not an ${\omega }$-covering]. Also we characterize the property of being an ${\omega }$-covering.
We prove the following theorems: There exists an ${\omega }$-covering with the property $s_0$. Under $\mathop {\mathrm cov}\nolimits ({\mathcal N}) = $ there exists $X$ such that $ \forall _{B \in {\mathcal B}or} [B\cap X$ is not an ${\omega }$-covering or $X\setminus B$ is not an ${\omega }$-covering]. Also we characterize the property of being an ${\omega }$-covering.
Classification : 03E15, 03E20, 28A05, 28E15
Keywords: ${\omega }$-covering set; ${\mathcal E}$; hereditarily nonparadoxical set 
@article{CMJ_2000_50_4_a13,
     author = {Nowik, Andrzej},
     title = {Some topological properties of $\omega$-covering sets},
     journal = {Czechoslovak Mathematical Journal},
     pages = {865--877},
     year = {2000},
     volume = {50},
     number = {4},
     mrnumber = {1792976},
     zbl = {1079.03547},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000_50_4_a13/}
}
TY  - JOUR
AU  - Nowik, Andrzej
TI  - Some topological properties of $\omega$-covering sets
JO  - Czechoslovak Mathematical Journal
PY  - 2000
SP  - 865
EP  - 877
VL  - 50
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2000_50_4_a13/
LA  - en
ID  - CMJ_2000_50_4_a13
ER  - 
%0 Journal Article
%A Nowik, Andrzej
%T Some topological properties of $\omega$-covering sets
%J Czechoslovak Mathematical Journal
%D 2000
%P 865-877
%V 50
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2000_50_4_a13/
%G en
%F CMJ_2000_50_4_a13
Nowik, Andrzej. Some topological properties of $\omega$-covering sets. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 865-877. http://geodesic.mathdoc.fr/item/CMJ_2000_50_4_a13/

[BJ] T. Bartoszyński, H. Judah: Borel images of sets of reals. Real Anal. Exchange 20(2) (1994/5), 536–558. | DOI | MR

[C] T. J. Carlson: Strong measure zero and strongly meager sets. Proc. Amer. Math. Soc. 118 (1993), 577–586. | DOI | MR | Zbl

[E] R. Engelking: General Topology, Revised and Completed Edition. Sigma Series in Pure Mathematics, vol. 6. Heldermann Verlag, Berlin, 1989. | MR

[K1] P. Komjáth: Large small sets. Colloq. Math. 56 (1988), 231–233. | DOI | MR

[K2] P. Komjáth: Some remarks on second category sets. Colloq. Math. 66 (1993), 57–62. | DOI | MR

[M] K. Muthuvel: Certain measure zero, first category sets. Real Anal. Exchange 17 (1991–92), 771–774. | MR

[P] M. Penconek: On nonparadoxical sets. Fund. Math. 139 (1991), 177–191. | DOI | MR | Zbl