# Article

 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 .

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