Zobrazeno 1 - 10
of 130
pro vyhledávání: '"Bardyla, Serhii"'
Autor:
Bardyla, Serhii, Zlatoš, Pavol
In this paper we investigate Schur ultrafilters on groups. Using the algebraic structure of Stone-\v{C}ech compactifications of discrete groups and Schur ultrafilters, we give a new description of Bohr compactifications of topological groups. This ap
Externí odkaz:
http://arxiv.org/abs/2409.07280
In this paper, we study an interplay between local and global properties of spaces of minimal usco maps equipped with the topology of uniform convergence on compact sets. In particular, for each locally compact space $X$ and metric space $Y$, we char
Externí odkaz:
http://arxiv.org/abs/2408.07409
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 many such topologies. Under containment, these Polish semigroup topolo
Externí odkaz:
http://arxiv.org/abs/2405.20134
In this paper, we show that the existence of certain first-countable compact-like extensions is equivalent to the equality between corresponding cardinal characteristics of the continuum. For instance, $\mathfrak b=\mathfrak s=\mathfrak c$ if and onl
Externí odkaz:
http://arxiv.org/abs/2404.09004
In this paper we study the behaviour of selective separability properties in the class of Frech\'{e}t-Urysohn spaces. We present two examples, the first one given in ZFC proves the existence of a countable Frech\'{e}t-Urysohn (hence $R$-separable and
Externí odkaz:
http://arxiv.org/abs/2305.17059
A family $\mathcal{A} \subseteq [\omega]^\omega$ such that for all finite $\{X_i\}_{i\in n}\subseteq \mathcal A$ and $A \in \mathcal{A} \setminus \{X_i\}_{i\in n}$, the set $A \setminus \bigcup_{i \in n} X_i$ is infinite, is said to be ideal independ
Externí odkaz:
http://arxiv.org/abs/2304.04651
In this paper, we investigate the poset $\mathbf{OF}(X)$ of free open filters on a given space $X$. In particular, we characterize spaces for which $\mathbf{OF}(X)$ is a lattice. For each $n\in\mathbb{N}$ we construct a scattered space $X$ such that
Externí odkaz:
http://arxiv.org/abs/2301.08704
Autor:
Banakh, Taras, Bardyla, Serhii
Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called (1) $\mathcal C$-$closed$ if $X$ is closed in every topological semigroup $Y\in\mathcal C$ containing $X$ as a discrete subsemigroup, (2) $ideally$ $\mathcal C$-$closed$
Externí odkaz:
http://arxiv.org/abs/2209.08013
Autor:
Banakh, Taras, Bardyla, Serhii
Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called $absolutely$ $\mathcal C$-$closed$ if for any homomorphism $h:X\to Y$ to a topological semigroup $Y\in\mathcal C$, the image $h[X]$ is closed in $Y$. Let $\mathsf{T_{\!1
Externí odkaz:
http://arxiv.org/abs/2207.12778
Autor:
Banakh, Taras, Bardyla, Serhii
In this paper we establish a connection between categorical closedness and topologizability of semigroups. In particular, for a class $\mathsf T_{\!1}\mathsf S$ of $T_1$ topological semigroups we prove that a countable semigroup $X$ with finite-to-on
Externí odkaz:
http://arxiv.org/abs/2111.14154