Mini-course (05.10.2023-23.11.2023, 6 lectures) - 3rd lecture:
During my third lecture I will present a description of a large class \(\mathcal{F}\) of filters on \(\omega\) such that for every \(F\in\mathcal{F}\) and every compact Hausdorff space \(K\) if the space \(\omega\cup\{F\}\) embeds into \(K\), then the Banach space \(C(K)\) is not a Grothendieck space. This will generalize a standard fact that if a space \(K\) contains a non-trivial convergent sequence, then \(C(K)\) is not Grothendieck.