Zobrazeno 1 - 10
of 286
pro vyhledávání: '"Zdomskyy, Lyubomyr"'
In this paper we investigate R-,H-, and M-{\it nw}-selective properties introduced in \cite{BG}. In particular, we provide consistent uncountable examples of such spaces and we define \textit{trivial} R-,H-, and M-{\it nw}-selective spaces the ones w
Externí odkaz:
http://arxiv.org/abs/2407.18713
We provide new techniques to construct sets of reals without perfect subsets and with the Hurewicz or Menger covering properties. In particular, we show that if the Continuum Hypothesis holds, then there are such sets which can be mapped continuously
Externí odkaz:
http://arxiv.org/abs/2406.12609
Using an iterated Sacks forcing and topological games, we prove that the existence of a totally imperfect Menger set in the Cantor cube with cardinality continuum, is independent from ZFC. We also analyze structures of Hurewicz or consonant subsets o
Externí odkaz:
http://arxiv.org/abs/2406.05457
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 only
Externí odkaz:
http://arxiv.org/abs/2404.09004
Autor:
Sobota, Damian, Zdomskyy, Lyubomyr
Improving a result of M. Talagrand, under the assumption of a weak form of Martin's axiom, we construct a totally disconnected compact Hausdorff space $K$ such that the Banach space $C(K)$ of continuous real-valued functions on $K$ is a Grothendieck
Externí odkaz:
http://arxiv.org/abs/2312.16155
All spaces are assumed to be Tychonoff. Given a realcompact space $X$, we denote by $\mathsf{Exp}(X)$ the smallest infinite cardinal $\kappa$ such that $X$ is homeomorphic to a closed subspace of $\mathbb{R}^\kappa$. Our main result shows that, given
Externí odkaz:
http://arxiv.org/abs/2310.17984
Using combinatorial covering properties, we show that there is no concentrated set of reals of size $\omega_2$ in the Miller model. The main result refutes a conjecture of Bartoszy\'{n}ski and Halbeisen. We also prove that there are no $\gamma$-set o
Externí odkaz:
http://arxiv.org/abs/2310.03864
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
Given a Tychonoff space $X$, we call a sequence $\langle\mu_n\colon n\in\omega\rangle$ of signed Borel measures on $X$ a finitely supported Josefson--Nissenzweig sequence (in short a JN-sequence) if: 1) for every $n\in\omega$ the measure $\mu_n$ is a
Externí odkaz:
http://arxiv.org/abs/2303.03809
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