High-dimensional sequential compactness

Abstract

We give examples of n-sequentially compact spaces that are not (n+1)-sequentially compact under several assumptions. We improve results of W. Kubiś and P. Szeptycki [Canad. Math. Bull. 66 (2023), 156–165] by building such examples from b=c and ♢(b)+d=ω1. We also introduce a new splitting-like cardinal invariant and then show that the same holds under s=b.