Countable compactness in powers of topological groups and Ramsey theoretic variations of compactness

Vinicius de Oliveira Rodrigues, Paul Jan Szeptycki, Artur Hideyuki Tomita

Countable compactness need not be preserved by finite products. Motivated by compactness notions for maps indexed by finite subsets of $\omega$, we introduce cascade countable compactne…