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${\omega }$-covering set; ${\mathcal E}$; hereditarily nonparadoxical set
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.
[BJ] T. Bartoszyński, H. Judah: Borel images of sets of reals. Real Anal. Exchange 20(2) (1994/5), 536–558. MR 1348078
[C] T. J. Carlson: Strong measure zero and strongly meager sets. Proc. Amer. Math. Soc. 118 (1993), 577–586. DOI 10.1090/S0002-9939-1993-1139474-6 | MR 1139474 | Zbl 0787.03037
[E] R. Engelking: General Topology, Revised and Completed Edition. Sigma Series in Pure Mathematics, vol. 6. Heldermann Verlag, Berlin, 1989. MR 1039321
[K1] P. Komjáth: Large small sets. Colloq. Math. 56 (1988), 231–233. MR 0991209
[K2] P. Komjáth: Some remarks on second category sets. Colloq. Math. 66 (1993), 57–62. MR 1242645
[M] K. Muthuvel: Certain measure zero, first category sets. Real Anal. Exchange 17 (1991–92), 771–774. MR 1171418
[P] M. Penconek: On nonparadoxical sets. Fund. Math. 139 (1991), 177–191. MR 1149411 | Zbl 0763.04005
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