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pro vyhledávání: '"primary 03E75"'
We work in the Baire space $\mathbb{Z}^\omega$ equipped with the coordinate-wise addition $+$. Consider a $\sigma-$ideal $\mathcal{I}$ and a family $\mathbb{T}$ of some kind of perfect trees. We are interested in results of the form: for every $A\in
Externí odkaz:
http://arxiv.org/abs/2409.17748
We work in the Cantor space $2^\omega$. The results of the paper adhere the following pattern. Let $\mathcal{I}\in \{\mathcal{M}, \mathcal{N}, \mathcal{M}\cap \mathcal{N}, \mathcal{E}\}$ and $T$ be a perfect, uniformly perfect or Silver tree. Then fo
Externí odkaz:
http://arxiv.org/abs/2405.13775
Autor:
Almontashery, Khulod, Szeptycki, Paul
We consider the relationship between normality and semi-proximality. We give a consistent example of a first countable locally compact Dowker space that is not semi-proximal, and two ZFC examples of semi-proximal non-normal spaces. This answers a que
Externí odkaz:
http://arxiv.org/abs/2311.00539
The motivation of this work are the two classical theorems on inscribing rectangles and squares into large subsets of the plane, namely Eggleston Theorem and Mycielski Theorem. Using Shoenfield Absoluteness Theorem we prove that for every Borel subse
Externí odkaz:
http://arxiv.org/abs/2307.07020
Autor:
Poór, Márk, Rinot, Assaf
In a paper from 1980, Shelah constructed an uncountable group all of whose proper subgroups are countable. Assuming the continuum hypothesis, he constructed an uncountable group $G$ that moreover admits an integer $n$ satisfying that for every uncoun
Externí odkaz:
http://arxiv.org/abs/2305.11155
Autor:
Bazzoni, Silvana, Šaroch, Jan
Enochs Conjecture asserts that each covering class of modules (over any ring) has to be closed under direct limits. Although various special cases of the conjecture have been verified, the conjecture remains open in its full generality. In this paper
Externí odkaz:
http://arxiv.org/abs/2303.08471
This paper introduced the concept of soft quasigroup, its parastrophes, soft nuclei, left (right) coset, distributive soft quasigroups and normal soft quasigroups. Necessary and sufficient conditions for a soft set over a quasigroup (loop) to be a so
Externí odkaz:
http://arxiv.org/abs/2207.06582
Publikováno v:
Topology Appl. 340 (2023), art. 108725, 15 pp
In this paper we construct consistent examples of subgroups of $2^\omega$ with Menger remainders which fail to have other stronger combinatorial covering properties. This answers several open questions asked by Bella, Tokgoz and Zdomskyy (Arch. Math.
Externí odkaz:
http://arxiv.org/abs/2205.00019
A $\sigma$-ideal $\mathcal{I}$ on a Polish group $(X,+)$ has Smital Property if for every dense set $D$ and a Borel $\mathcal{I}$-positive set $B$ the algebraic sum $D+B$ is a complement of a set from $\mathcal{I}$. We consider several variants of th
Externí odkaz:
http://arxiv.org/abs/2102.03287
Autor:
Corson, Samuel M.
Publikováno v:
Pacific J. Math. 327 (2023) 297-336
It is shown that the fundamental group of the Griffiths double cone space is isomorphic to that of the triple cone. More generally if $\kappa$ is a cardinal such that $2 \leq \kappa \leq 2^{\aleph_0}$ then the $\kappa$-fold cone has the same fundamen
Externí odkaz:
http://arxiv.org/abs/2012.06794