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On the surface, the definitions of chainability and Lebesgue covering dimension â‰¤ 1 are quite similar as covering properties. Using the ultracoproduct construction for compact Hausdorff spaces, weâ€¦ (More)

- Taras O. Banakh, Nadia Lyaskovska
- IJAC
- 2008

Answering a question of D.Dikranjan and I.Protasov we prove that each infinite group G contains a weakly P-small subset A âŠ‚ G which is not P-small. This means that for every n there are n pairwiseâ€¦ (More)

We introduce and study varions notions of completeness of translation-invariant ideals in groups. In this paper we introduce and study various notions of completeness of translation-invariant idealsâ€¦ (More)

- Taras O. Banakh
- 2008

We introduce and study (metrically) quarter-stratifiable spaces and then apply them to generalize Rudin and Kuratowski-Montgomery theorems about the Baire and Borel complexity of separatelyâ€¦ (More)

- Taras O. Banakh, Artem Dudko, Dusan Repovs
- Discrete Mathematics & Theoretical Computerâ€¦
- 2010

We prove that for each partition of the Lobachevsky plane into finitely many Borel pieces one of the cells of the partition contains an unbounded centrally symmetric subset. It follows from [B1] (seeâ€¦ (More)

- Taras O. Banakh, BOHDAN BOKALO, IGOR GURAN, MICHAEL ZARICHNYI, Ivan Franko
- 2006

We recall that a metric space X is proper if the distance d(Â·, x0) to a fixed point is a proper map for any x0 âˆˆ X. A map f : X â†’ Y between metric spaces is called coarse if it satisfies theâ€¦ (More)

Assuming the absence of Q-points (which is consistent with ZFC) we prove that the free topological group F (X) over a Tychonov space X is o-bounded if and only if every continuous metrizable image Tâ€¦ (More)

We prove that the number of near-coherence classes of non-principal ultrafilters on the natural numbers is either finite or 2c. Moreover, in the latter case the Stone-ÄŒech compactification Î²Ï‰ of Ï‰â€¦ (More)

- Taras O. Banakh, Nadia Lyaskovska, Dusan Repovs
- Notre Dame Journal of Formal Logic
- 2009

For a subset A of a Polish group G, we study the (almost) packing index indP (A) (resp. IndP (A)) of A, equal to the supremum of cardinalities |S| of subsets S âŠ‚ G such that the family of shiftsâ€¦ (More)

- Taras O. Banakh, Oleg Verbitsky, Yaroslav Vorobets
- Electr. J. Comb.
- 2000

Given a space Î© endowed with symmetry, we define ms(Î©, r) to be the maximum of m such that for any r-coloring of Î© there exists a monochromatic symmetric set of size at least m. We consider a wideâ€¦ (More)