Let $X$ be a compact Hausdorff topological space whose convergent sequences are eventually constant. Is there a description of such spaces. How ''far'' these spaces from Stonean ones?
2026-04-13 21:01:54.1776114114
When only eventually constant sequences are convergent?
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Norbert, I don't think that there is a reasonable description of such spaces. Indeed, they properly contain spaces $K$ for which the Banach space $C(K)$ is Grothendieck and this class is far from being fully delineated. For example, there are connected, compact spaces $K$ for which $C(K)$ is indecomposable, hence Grothendieck.