| Title:
|
Some topological properties of $\omega$-covering sets (English) |
| Author:
|
Nowik, Andrzej |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
865-877 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
${\omega }$-covering set |
| Keyword:
|
${\mathcal E}$ |
| Keyword:
|
hereditarily nonparadoxical set |
| MSC:
|
03E15 |
| MSC:
|
03E20 |
| MSC:
|
28A05 |
| MSC:
|
28E15 |
| idZBL:
|
Zbl 1079.03547 |
| idMR:
|
MR1792976 |
| . |
| Date available:
|
2009-09-24T10:38:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127616 |
| . |
| Reference:
|
[BJ] T. Bartoszyński, H. Judah: Borel images of sets of reals.Real Anal. Exchange 20(2) (1994/5), 536–558. MR 1348078, 10.2307/44152538 |
| Reference:
|
[C] T. J. Carlson: Strong measure zero and strongly meager sets.Proc. Amer. Math. Soc. 118 (1993), 577–586. Zbl 0787.03037, MR 1139474, 10.1090/S0002-9939-1993-1139474-6 |
| Reference:
|
[E] R. Engelking: General Topology, Revised and Completed Edition. Sigma Series in Pure Mathematics, vol. 6.Heldermann Verlag, Berlin, 1989. MR 1039321 |
| Reference:
|
[K1] P. Komjáth: Large small sets.Colloq. Math. 56 (1988), 231–233. MR 0991209, 10.4064/cm-56-2-231-233 |
| Reference:
|
[K2] P. Komjáth: Some remarks on second category sets.Colloq. Math. 66 (1993), 57–62. MR 1242645, 10.4064/cm-66-1-57-62 |
| Reference:
|
[M] K. Muthuvel: Certain measure zero, first category sets.Real Anal. Exchange 17 (1991–92), 771–774. MR 1171418 |
| Reference:
|
[P] M. Penconek: On nonparadoxical sets.Fund. Math. 139 (1991), 177–191. Zbl 0763.04005, MR 1149411, 10.4064/fm-139-3-177-191 |
| . |
