Seminarium:
Topologia
Osoba referująca:
Tomasz Żuchowski (UWr)
Data:
wtorek, 23. Kwiecień 2024 - 17:00
Sala:
A.4.1 C-19 (Politechnika Wrocławska)
Opis:
In this talk we will continue studying the family $\mathcal{AN}$ of
ideals on $\omega$ presented in the Part I. Recall that
$\mathcal{I}\in\mathcal{AN}$ iff there exists a density submeasure
$\varphi$ on $\omega$ such that $\varphi(\omega)=\infty$ and
$\mathcal{I}\subseteq Exh(\varphi)$.
We will present several conditions for a density ideal $\mathcal{I}$
equivalent to the fact that $\mathcal{I}\in\mathcal{AN}$. Next, we will
make an analysis of the cofinal structure of the family $\mathcal{AN}$
ordered by the Katetov order $\leq_K$. We will prove that there is a
family of size $\mathfrak{d}$ which is $\leq_K$-dominating in
$\mathcal{AN}$, but there are no $\leq_K$-maximal elements in
$\mathcal{AN}$.