High Dimensional Sequential Compactness

We will study high dimensional generalizations of sequential compactness. In the first part, we will give some background and focus on the finite case. Following the study started by Kubis and Szeptycki, we will present some results and counterexamples. In the second part we will step up to the infinite case, extend some results from the finite case and relate these new notions to classical ones, as well as to present some applications.