We give examples of $ n $-sequentially compact spaces that are not $(n+ 1) $-sequentially
compact under several assumptions. We improve results from Kubis and Szeptycki by …

For many years, there have been conducting research (eg, by Bergelson, Furstenberg,
Kojman, Kubiś, Shelah, Szeptycki, Weiss) into sequentially compact spaces that are, in a …

For a free filter F on ω, let NF= ω∪{p F}, where p F∉ ω, be equipped with the following
topology: every element of ω is isolated whereas all open neighborhoods of p F are of the …

arxiv:1708.05322v1 [math.LO] 17 Aug 2017 Page 1 arxiv:1708.05322v1 [math.LO] 17 Aug
2017 NO MINIMAL TALL BOREL IDEAL IN THE KATETOV ORDER JAN GREBÍK1 AND …

A family I of subsets of a set X is an ideal on X if it is closed under taking subsets and finite
unions of its elements. An ideal I on X is below an ideal J on Y in the Katetov order if there is …

Abstract A family\(\mathcal {I}\) of subsets of a set X is an ideal on X if it is closed under
taking subsets and finite unions of its elements. An ideal\(\mathcal {I}\) on X is below an …

For a family F⊆ ω ω we define the ideal I (F) on ω× ω to be the ideal generated by the family
{A⊆ ω× ω:∃ f∈ F∀∞ n (|{k:(n, k)∈ A}|≤ f (n))}. Using ideals of the form I (F), we show that …

We construct an embedding of the algebra P (ω)/Fin into the family of summable ideals with
the Katětov order. This construction will be used to solve two problems: about the relation …

We continue with the study of the Katětov order on MAD families. We prove that Katětov
maximal MAD families exist under This improves previously known results from the …

We show that there is a Σ 4 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}
\usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} …