7 papers
New approaches to remote points
Serhii Bardyla, Jaroslav Å upina
For a given Tychonoff space , a point is called {\em remote} if is not in the closure of any nowhere dense subset of . In this paper, we character…
Polish topologies on endomorphism monoids of linear orders
Serhii Bardyla, Luna Elliott
In this paper, we investigate Polish semigroup topologies on the endomorphism monoids and . We introduce…
Countably compact inverse semigroups and Nyikos' problem
Serhii Bardyla
A regular separable first-countable countably compact space is called a Nyikos space. In this paper, we give a partial solution to an old problem of Nyikos by showing that each loc…
A note on intrinsic topologies of groups
S. Bardyla, L. Elliott, J. D. Mitchell +1
We investigate topologies on groups which arise naturally from their algebraic structure, including the Frechét-Markov, Hausdorff-Markov, and various kinds of Zariski topologies.…
Schur ultrafilters and Bohr compactifications of topological groups
Serhii Bardyla, Pavol Zlatoš
In this paper we investigate Schur ultrafilters on groups. Using the algebraic structure of Stone-Äech compactifications of discrete groups and Schur ultrafilters, we give a new d…
Classifying the Polish semigroup topologies on the symmetric inverse monoid
Serhii Bardyla, Luna Elliott, James Mitchell +1
We classify all Polish semigroup topologies on the symmetric inverse monoid on the natural numbers. This result answers a question of Elliott et al. There are countably infinitely…